The GiC (IPA: /ɡiːk/) seminar is an algebraic geometry seminar for those in and around Cardiff area and, more generally, in the southwest. All are welcome. The seminar meets on Wednesday afternoons 16:00 - 18:00 UK Time, normally in M/2.06. For the moment, owing to the pandemic, we meet online via Zoom.

The subjects of the talks reflect the interests of its current organisers, ranging from the classical algebraic geometry to all things derived, categorical and homotopical. The talks are sometimes followed by a social dinner for the participants.

Please address any questions or queries to one of the seminar organisers:

• Dr. Timothy Logvinenko  LogvinenkoT at cardiff ac uk
• Mr. Oscar Finegan  Finegan at cardiff ac uk

In particular, contact Dr. Timothy Logvinenko if you wish to be added to the GiC Seminar mailing list.

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Next Meeting:

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• Date:	Wed 12th June, 2024
  Place:	Abacws/2.26
  14:00-15:00	Arman Sarikyan (Edinburgh)
  “Equivariant birational geometry”
  Equivariant birational geometry is a subject of algebraic geometry that studies (birational) group actions on algebraic varieties. One of the main questions it addresses is: given two algebraic varieties \(X\) and \(Y\), with an action of a group \(G\), can we find an isomorphism between their open and dense subsets that is compatible with the action of \(G\)? Surprisingly, equivariant birational geometry finds a lot of applications even outside of algebraic geometry, for example in number theory or group theory. This talk will provide an introduction to general ideas of equivariant birational geometry and their applications. We will see how some purely group theoretic questions can be translated into geometric ones, allowing us to approach them from a different angle.
  16:00-17:00	Rudradip Biswas (Warwick)
  “ Bounded t-structures on derived categories of schemes - new results and generalizations”
  Bounded t-structures are an important tool in studying triangulated categories. Of course, not all triangulated categories admit bounded t-structures, so in general, results providing general obstructions to the existence of bounded t-structures are usually very useful. I will talk about a new obstruction result for bounded t-structures that I recently proved in a project with Hongxing Chen, K Manali Rahul, Chris Parker, and Junhua Zheng (arxiv:2401.00130). In short, we show that for any triangulated category satisfying a small finiteness property, the existence of a bounded t-structure on it forces it to be equal to its "completion". My focus will be on the new results that we can derive for (a) the category of perfect complexes over a scheme, and (b) the bounded derived category of complexes with coherent cohomology over finite-dimensional Noetherian schemes. In short, for (a), we show that if the category of perfect complexes has a bounded t-structure, then it should be equal to its completion. I will mention in detail what this "completion" is; this result actually improves and generalizes, with different methods, a deep result by Amnon Neeman ("Bounded t-structures on perfect complexes", to appear in Acta Math) where he proved this for Noetherian schemes settling a big conjecture by Antieau-Gepner-Heller. His method is exclusive to the case of perfect complexes and does not use completions. The categories in (b) always have at least one bounded t-structure - we show, again obtaining a big improvement on a collection of theorems of Neeman's from the same paper, that there is only one bounded t-structure in these categories up to "equivalence". This notion of "equivalence" is new, although flavours of it have occurred before in the work of Polishchuk. If time permits, I will talk about how this notion of equivalence connects to studying some properties of the stability manifold.

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Future Meetings:

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No further meetings have been scheduled at this time.

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Past Meetings:

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• Date:	Wed 1st May, 2024
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXXXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the upper semicontinuity theorem. We continue to look at the cohomologies of a sheaf twisted by a pullback from an affine scheme.

• Date:	Wed 24th April, 2024
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXXXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the upper semicontinuity theorem. We begin by looking at the cohomologies of a sheaf twisted by a pullback from an affine scheme.

• Date:	Wed 3rd April, 2024
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXXXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at look at the exercised after after Chapter III.11 (The Theorem on Formal Functions).

• Date:	Wed 20th March, 2024
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXXXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the theorem on formal functions.

• Date:	Wed 6th March, 2024
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXXXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the theorem on formal functions.

• Date:	Wed 21st February, 2024
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXXXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we will look at the exercised after after Chapter III.10 (Smooth Morphisms).

• Date:	Wed 7th February, 2024
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXXXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at smooth morphisms of schemes and consider group varieties and homogeneous spaces.

• Date:	Wed 31st January, 2024
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXXXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at smooth morphisms of schemes and examine smooth morphisms of nonsingular varieties.

• Date:	Wed 24th January, 2024
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXXX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we start lookng at smooth morphisms of schemes.

• Date:	Wed 6th December, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the exercises after Chapter III.9 (Flat Morphisms).

• Date:	Wed 29th November, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, and look at infinitesimal deformations of schemes.

• Date:	Wed 15th November, 2023
  Place:	Cardiff School of Mathematics, Abacws/1.04 (in person)
  16:00-17:30	Alexey Elagin (Edinburgh)
  “New achievements in categorical algebraic geometry”
  In this overview talk I will tell you about three long-standing questions in categorical algebraic geometry that have been answered in the last year. All answers appear to be rather elementary and some – even surprising. First, Olander and Pirozhkov proved the following conjecture due to Orlov: for algebraic varieties \(X\) and \(Y\), if the derived category \(D^b(X)\) embeds fully faithful into \(D^b(Y)\) then the dimension of \(X\) is less or equal to the dimension of \(Y\). This follows directly from considering the invariant of a triangulated category called countable Rouquier dimension, which has been successfully computed for quasi-projective varieties. Second, Krah constructed a phantom subcategory in the derived category of a rational surface. This phantom subcategory has zero Grothendieck group and is constructed as the orthogonal to an exceptional collection of maximal length that is not full. Third, Chang, Haiden, and Schroll provided counterexamples to an old conjecture by Bondal and Polishchuk stating that the braid group action on the set of full exceptional collections in a triangulated category is transitive.

• Date:	Wed 8th November, 2023
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, and look at infinitesimal deformations of schemes.

• Date:	Wed 25th October, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, starting with the behaviour of the Hilbert polynomial in an algebraic family.

• Date:	Wed 11th October, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, starting with numerical properties of flat families of varieties.

• Date:	Wed 4th October, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, starting with algebraic families of divisors.

• Date:	Wed 27th September, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, starting with the notion of passing to the limit of a flat family over a punctured curve.

• Date:	Wed 20th September, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families, starting with the dimension of a fiber in flat family.

• Date:	Wed 6th September, 2023
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms and flat families.

• Date:	Wed 16th August, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms, starting with the notion of a flat family.

• Date:	Wed 9th August, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at flat morphisms, starting with the definition of a sheaf flat over a morphism of schemes.

• Date:	Wed 2nd August, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we will start looking at flat morphisms.

• Date:	Wed 26th July, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at the higher direct images of sheaves.

• Date:	Wed 19th July, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we will start looking at the higher direct images of sheaves.

• Date:	Wed 12th July, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we will work our way through the exercises after Chapter III.7 (The Serre Duality Theorem).

• Date:	Wed 14th June, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at the Serre Duality theorem, starting with the dualising sheaves of projective varieties and subvarieties.

• Date:	Wed 7th June, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at the Serre Duality theorem, starting with the lemma of Enriques-Severi-Zariski.

• Date:	Wed 31st May, 2023
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at the Serre Duality theorem.

• Date:	Wed 26th Apr, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue with our introduction to the Serre Duality theorem.

• Date:	Wed 19th Apr, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we take a detour to give a basic introduction to Koszul complexes.

• Date:	Wed 29th Mar, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue with our introduction to the Serre Duality theorem.

• Date:	Wed 15th Mar, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we begin looking at the Serre Duality theorem.

• Date:	Wed 8th Mar, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardif)
  “Sheaf Cohomology XVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we finish looking at Ext groups and sheaves, as well as explain the reason behind their name.

• Date:	Wed 1st Mar, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue to look at Ext groups and sheaves, starting with some of their properties regarding locally free sheaves of finite rank.

• Date:	Wed 22nd Feb, 2023
  Place:	Zoom @ online
  16:00-17:30	Charlotte Bartram (Glasgow)
  “Sheaf Cohomology XV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue to look at Ext groups and sheaves, starting with the long exact sequences associated to them.

• Date:	Wed 15th Feb, 2023
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology XIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at Ext groups and sheaves, starting with the definition of local and global Ext functors.

• Date:	Wed 8th Feb, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology XIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we work our way through the exercises in the end of the section III.5 (The Cohomology of Projective Space).

• Date:	Wed 1st Feb, 2023
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology XII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at the sheaf cohomology of invertible sheaves on a projective space, beginning with the cohomological criterion for ampleness.

• Date:	Wed 25th Jan, 2023
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology XI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we start looking at the sheaf cohomology of invertible sheaves on a projective space.

• Date:	Wed 18th Jan, 2023
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology X”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we work our way through the exercises in the end of the section III.4 (Cech Cohomology).

• Date:	Wed 14th Dec, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology IX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we continue looking at Cech cohomology.

• Date:	Wed 30th Nov, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology VIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we start looking at Cech cohomology.

• Date:	Wed 16th Nov, 2022
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Sheaf Cohomology VII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the notions of depth of an ideal and associated primes of a module.

• Date:	Wed 9th Nov, 2022
  Place:	Zoom @ online
  16:00-17:30	Charlotte Bartram (Glasgow)
  “Sheaf Cohomology VI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the exercises at the end of the Section III.3 (Cohomology of a Noetherian Affine Scheme).

• Date:	Wed 2nd Nov, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology V”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we finish looking at the exercises at the end of the Section III.2 (Cohomology of Sheaves).

• Date:	Wed 26th Oct, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Sheaf Cohomology IV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at the exercises at the end of the Section III.2 (Cohomology of Sheaves).

• Date:	Wed 19th Oct, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Sheaf Cohomology III”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we start looking at cohomology of sheaves.

• Date:	Wed 12th Oct, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Sheaf Cohomology II”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at some basics of homological algebra, such as δ-functors.

• Date:	Wed 5th Oct, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Sheaf Cohomology I”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 3 of Hartshorne's “Algebraic geometry”, covering the basics of sheaf cohomology. In this talk, we look at some basics of homological algebra, starting with the notion of an abelian category.

• Date:	Wed 28th Sep, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXXXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish looking at the formal schemes.

• Date:	Wed 7th Sep, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXXXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue looking at formal schemes, beginning with ideals of definition.

• Date:	Wed 31st Aug, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXXXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start looking at formal schemes, beginning with the notion of the formal completion of a scheme along a closed subscheme.

• Date:	Wed 24th Aug, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXXXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start looking at formal schemes, beginning with the notion of the completion with respect to an ideal.

• Date:	Wed 10th Aug, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXXXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start looking at formal schemes, beginning with the notion of the inverse limit.

• Date:	Wed 3rd Aug, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXXXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish looking at the exercises at the end of the Section II.8 (Differentials).

• Date:	Wed 27th Jul, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXXX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to look at the exercises at the end of the Section II.8 (Differentials).

• Date:	Wed 20th Jul, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to look at the exercises at the end of the Section II.8 (Differentials).

• Date:	Wed 13th Jul, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at the exercises at the end of the Section II.8 (Differentials).

• Date:	Wed 6th Jul, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at blowups of smooth varieties in smooth centers.

• Date:	Wed 22nd June, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at some local algebra and the geometrical notion of being a local complete intersection.

• Date:	Wed 8th June, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish looking at applications of the results we established for sheaves of differentials on non-singular varieties, and then look at some local algebra.

• Date:	Wed 1st June, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at some applications of the results we established for sheaves of differentials on non-singular varieties.

• Date:	Wed 18th May, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at sheaves of differentials on non-singular varieties.

• Date:	Wed 11th May, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at sheaves of differentials on schemes.

• Date:	Wed 4th May, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at generic and local properties of Kähler differentials.

• Date:	Wed 27th Apr, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish working through the exercises at the end of the Section II.7 (Projective Morphisms) and begin looking at the algebraic notion of Kähler differentials.

• Date:	Wed 20th Apr, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish working through the exercises at the end of the Section II.7 (Projective Morphisms) and begin looking at the algebraic notion of Kähler differentials.

• Date:	Wed 13th Apr, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath) and Oscar Finegan (Cardiff)
  “Scheme Theory LXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue working through the exercises at the end of the Section II.7 (Projective Morphisms).

• Date:	Wed 6th Apr, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue working through the exercises at the end of the Section II.7 (Projective Morphisms).

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• Date:	Wed 30th Mar, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start working through the exercises at the end of the Section II.7 (Projective Morphisms).

• Date:	Wed 16th Mar, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at the blowing up construction, starting with the result that any birational projective morphism of quasi-projective varieties can be written as a blowup.

• Date:	Wed 9th Mar, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at the blowing up construction, starting with its universal property.

• Date:	Wed 2nd Mar, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we look at projective space bundles.

• Date:	Wed 23rd Feb, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start looking at the relative Proj construction.

• Date:	Wed 16th Feb, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start looking at linear systems on smooth projective varieties.

• Date:	Wed 9th Feb, 2022
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory LX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue at ample invertible sheaves, beginning with some examples.

• Date:	Wed 2nd Feb, 2022
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue looking at morphisms from a scheme into a projective space, starting with ample invertible sheaves.

• Date:	Wed 26th Jan, 2022
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue looking at morphisms from a scheme into a projective space. We begin with an example of the rational morphism defined by a collection of line bundle sections which isn't globally generating.

• Date:	Wed 19th Jan, 2022
  Place:	Zoom @ online
  16:00-17:30	Austin Hubbard (Bath)
  “Scheme Theory LVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we begin looking at morphisms from a scheme into a projective space.

• Date:	Wed 12th Jan, 2022
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory LVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish working through the exercises at the end of the Section II.6 (Divisors).

• Date:	Wed 15th Dec, 2021
  Place:	Zoom @ online
  16:00-17:30	Ed Segal (UCL)
  “A survey of hybrid models”
  The Kuznetsov component of a Fano complete intersection can be realized as a `hybrid model' - a category of matrix factorizations on a vector bundle over weighted projective space. I'll explain what all this means, and then discuss some cases where the hybrid model description can give us some geometric insight into the category.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory LV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to work through the exercises at the end of the Section II.6 (Divisors).

• Date:	Wed 1st Dec, 2021
  Place:	Zoom @ online
  16:00-17:30	Federico Barbacovi (UCL)
  “Spherical functors and the flop-flop autoequivalence” Video recording (YouTube)
  Bondal—Orlov, Kawamata conjecture predicts that certain birational transformations called flops should induce derived equivalences. Using such equivalences we can construct autoequivalences of derived categories which go under the name of flop-flop autoequivalences. In this talk I will explain how to realise the flop-flop autoequivalence as (the inverse of) a spherical twist around a spherical functor, thus repackaging the so-called flop-flop = twist formulas in a single framework. We will also survey some examples of this construction where a splitting of the flop-flop autoequivalence can be read off from the source category of the spherical functor.
  17:30-18:15	Wing Kei Poon (Bath)
  “Scheme Theory LIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to work through the exercises at the end of the Section II.6 (Divisors).

• Date:	Wed 24th Nov, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory LIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss divisors on schemes, beginning with some remarks about closed subschemes of codimension one on a scheme X.

• Date:	Wed 17th Nov, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory LII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss divisors on schemes, beginning with the notion of the invertible sheaf associated to a divisor.

• Date:	Wed 10th Nov, 2021
  Place:	Zoom @ online
  16:00-17:30	Sophia Restad (Kansas)
  “Composing Spherical Twists” Video recording (YouTube)
  F. Barbacovi proved that the composition of two spherical twists can itself arise as a spherical twist, with a natural choice of a source category. We examine this construction further. The construction is based around gluing two dg categories along a certain bimodule. A natural question to ask is whether the gluing can be improved, i.e. if choosing a different bimodule can lead to a possibly simpler source category. We prove the answer is essentially no.
  17:30-18:15	Calla Tschanz (Bath)
  “Scheme Theory LI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss divisors on schemes, beginning with the notion of invertible sheaves.

• Date:	Wed 3rd Nov, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory L”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of Cartier divisors.

• Date:	Wed 27th Oct, 2021
  Place:	Zoom @ online
  16:00-17:30	Arman Sarikyan (Edinburgh)
  “Scheme Theory XLIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of Weil divisors on algebraic curves, beginning with the divisor class group of the nonsingular cubic curve.

• Date:	Wed 13th Oct, 2021
  Place:	Zoom @ online
  16:00-17:30	Arman Sarikyan (Edinburgh)
  “Scheme Theory XLVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of Weil divisors on algebraic curves, beginning with a technical result on morphisms from a nonsingular curve to an arbitrary curve.

• Date:	Wed 6th Oct, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XLVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of divisor, and the divisor class group of a nonsingular quadric surface in P^3.

• Date:	Wed 29th Sep, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XLVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of divisor, beginning with the divisor class group of a nonsingular quadric surface in P^3.

• Date:	Wed 22nd Sep, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory XLV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of divisor, beginning with the divisor class group of an affine line fibration.

• Date:	Wed 8th Sep, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XLIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of divisor, beginning with the properties of the divisor class group.

• Date:	Wed 1st Sep, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XLIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we discuss the notion of divisor, beginning with an informal example.

• Date:	Wed 25th Aug, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XLII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish discussing the exercises offered by Hartshorne on the subject of sheaves of modules on a ringed space.

• Date:	Wed 18th Aug, 2021
  Place:	Zoom @ online
  16:00-17:30	Arman Sarikyan (Edinburgh)
  “Scheme Theory XLI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing the exercises offered by Hartshorne on the subject of sheaves of modules on a ringed space.

• Date:	Wed 11th Aug, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XL”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing the exercises offered by Hartshorne on the subject of sheaves of modules on a ringed space.

• Date:	Wed 4th Aug, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XXXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing the exercises offered by Hartshorne on the subject of sheaves of modules on a ringed space.

• Date:	Wed 28th Jul, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XXXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing the exercises offered by Hartshorne on the subject of sheaves of modules on a ringed space.

• Date:	Wed 21st Jul, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “The Heisenberg category of a category, III” Video recording (YouTube)
  In this series of three talks we discuss how to associate a Heisenberg category to any smooth and proper dg category. In this final talk, we will present the DG categorical version of our construction, comparing it to the additive case construction discussed in the previous talk. The main challenge here is a lack of the genuine Serre functor, and thus the necessity of working with a homotopy one. We will discuss the unique features of our construction introduced to overcome this and the other challenges we encountered. We will also discuss the applications, as well as the reasons for working in the DG setting in the first place. This is joint work with Ádám Gyenge and Clemens Koppensteiner.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory XXXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we finish our discussion of sheaves of modules on a ringed space by considering the exercises provided by Hartshorne on this topic.

• Date:	Wed 14th Jul, 2021
  Place:	Zoom @ online
  16:00-17:30	Ádám Gyenge (Alfréd Rényi, Budapest)
  “The Heisenberg category of a category, II” Video recording (YouTube) Talk slides (PDF)
  Khovanov introduced recently a categorification of the infinite Heisenberg algebra associated with the free boson or, equivalently, a rank 1 lattice, using a graphical construction involving planar diagrams. We extend Khovanov’s graphical construction to derived categories of smooth and projective varieties or, more generally, to categories having a Serre functor. In our case the underlying lattice will be the (numerical) Grothendieck group of the category. We also obtain a 2-representation of our Heisenberg category on a categorical analogue of the Fock space. Joint work with Clemens Koppensteiner and Timothy Logvinenko.
  17:30-18:15	Wing Kei Poon (Bath)
  “Scheme Theory XXXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss sheaves of modules on a ringed space, beginning with the statement that coherent sheaves on a projective scheme can be written as a quotient of a direct sum of twisted structure sheaves O(n).

• Date:	Wed 7th Jul, 2021
  Place:	Zoom @ online
  16:00-17:30	Clemens Koppensteiner (Oxford)
  “The Heisenberg category of a category, I” Video recording (YouTube)
  In this series of three talks we will discuss how to associate a Heisenberg category to any smooth and proper dg category. In this first introductory talk, we will consider the geometric motivation for the construction, review the theory of Heisenberg algebras, and look at some categorifications already in the literature. This is joint work with Ádám Gyenge and Timothy Logvinenko.
  17:30-18:15	Calla Tschanz (Bath)
  “Scheme Theory XXXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss sheaves of modules on a ringed space, beginning with sheaves generated by global sections.

• Date:	Wed 30th Jun, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory XXXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with very ample sheaves.

• Date:	Wed 23rd Jun, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XXXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with the statement that a scheme is projective if and only if it is isomorphic to the Proj of a graded ring finitely generated in degree 1.

• Date:	Wed 16th Jun, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XXXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with the graded modules associated to quasi-coherent sheaves on a Proj of a graded ring.

• Date:	Wed 9th Jun, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XXXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with quasi-coherent sheaves on a Proj of a graded ring.

• Date:	Wed 2nd Jun, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory XXX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with the properties of ideal sheaves.

• Date:	Wed 26th May, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XXIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space, starting with the exactness of the global sections functor on quasi-coherent sheaves on an affine scheme.

• Date:	Wed 19th May, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XXVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space starting with quasi-coherent sheaves.

• Date:	Wed 12th May, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XXVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discussing sheaves of modules on a ringed space starting with free and locally free sheaves.

• Date:	Wed 5th May, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory XXVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we start on the notion of a sheaf of modules on a ringed space.

• Date:	Wed 28th Apr, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XXV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with the notion of an abstract variety.

• Date:	Wed 21st Apr, 2021
  Place:	Zoom @ online
  16:00-17:30	Miles Reid (Warwick)
  “ The Tate-Oort group TO_p and moduli of Godeaux surfaces” Video recording (YouTube)
  The Tate-Oort group scheme TO_p is a group scheme of order p defined in mixed characteristic at p. It contains the cyclic groups ℤ/p and μ_p in characteristic 0, and the three group schemes ℤ/p, μ_p, and α_p in characteristic p. Godeaux surfaces X in characteristic 5 with ℤ/5, μ_5, and α_5 in Pic X were constructed respectively by Lang, Miranda and Liedtke as quotients of quintic surfaces Y_5 in ℙ^3 equivariant under an action of the dual group schemes μ_5, ℤ/5, and α_5. All three of these constructions can be put together in a single deformation family, together with the classical Godeaux surfaces. This is joint work with KIM Soonyoung, based in part on her 2014 Sogang Univ. thesis. See also https://homepages.warwick.ac.uk/~masda/TOp/.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory XXIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with basic properties of proper morphisms.

• Date:	Wed 14th Apr, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XXIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with valuative criterion for properness.

• Date:	Wed 7th Apr, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XXII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with basic properties of separated morphisms.

• Date:	Wed 31st Mar, 2021
  Place:	Zoom @ online
  16:00-17:30	Timothy Logvinenko (Cardiff)
  “Scheme Theory XXI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with basic properties of separated morphisms.

• Date:	Wed 24th Mar, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, finishing the proof of the valuatative criterion for separatedness.

• Date:	Wed 17th Mar, 2021
  Place:	Zoom @ online
  16:00-17:30	David Favero (Alberta)
  “Geometric invariant theory through group compactifications, derived categories, and derived algebraic geometry” Video recording (YouTube)
  Given a group G acting on an algebraic variety X, geometric invariant theory tells us how to get a (or several) nice quotient space(s) from this data. Traditionally, this comes from the choice of a G-equivariant line bundle on X. I will discuss an alternative approach via partially compactifying the action groupoid. One benefit of this viewpoint is that it produces a natural correspondence between X and itself. This allows us to embedd the derived category of a given GIT quotient in the derived category of [X/G] and make comparisons (and sometimes deduce equivalences) between derived categories of (the several) GIT quotients. If time permits, I will also discuss how to use this approach in the singular setting through the lens of derived algebraic geometry.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory XIX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss separated and proper morphisms of schemes, beginning with the valuatative criterion for separatedness.

• Date:	Wed 10th Mar, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XVIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss first properties of schemes beginning with the discussion of base extensions.

• Date:	Wed 3rd Mar, 2021
  Place:	Zoom @ online
  16:00-17:30	Yan Soibelman (Kansas)
  “Algebra of the infrared and Fukaya-Seidel categories with coefficients in perverse schobers” Talk notes (PDF) Video recording (YouTube)
  Several years ago physicists Gaitto,Moore and Witten discovered a remarkable algebraic structure underlying all 2d N=(2,2) QFTs. They call it "the algebra of the infrared". Mathematical byproduct of that work was an alternative definition of the Fukaya-Seidel category (= Landau-Ginzburg model) of a Kahler manifold. It is given in terms of the critical points of the superpotential of the LG-model and gradient trajectories between them. In the joint paper with Kapranov and Kontsevich we interpreted the algebraic structure of Gaiotto-Moore-Witten in terms of L-infinity and A-infinity algebras associated with the secondary polytope of the convex hull of the set of critical values of the superpotential. In my talk I will explain how our approach can be generalized to the case of Fukaya-Seidel categories with coefficients which are perverse schobers. The talk is based on the recent work, joint with Kapranov and Soukhanov.

• Date:	Wed 24th Feb, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XVII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discuss first properties of schemes starting with the proof that fibre products exist.

• Date:	Wed 17th Feb, 2021
  Place:	Zoom @ online
  16:00-17:30	Sergey Arkhipov (Aarhus)
  “Differential forms with logarithmic singularities and categorical braid group actions”
  Bezrukavnikov and Riche studied the affine Hecke category - a categorification of the affine braid group. One realization of this category is via equivariant coherent sheaves on the Steinberg variety. Braid group generators are provided by explicit coherent sheaves. However, braid relations are proved in a rather indirect way - either by a case by case analysis or by reduction to prime characteristic. Using linear Koszul duality, we propose another realization of the affine Hecke category via equivariant Omega-modules on the corresponding simple algebraic group G. A study of logarithmic differential forms on Bott-Samelson varieties gives a simple and uniform proof of braid relations. The material of the talk is a joint work in progress with my student Sebastian Orsted.
  17:30-18:15	Timothy Logvinenko (Cardiff)
  “Scheme Theory XVI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discuss first properties of schemes, beginning with fibre products.

• Date:	Wed 10th Feb, 2021
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory XV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discuss first properties of schemes, continuing with the examples of open and closed immersions.

• Date:	Wed 3rd Feb, 2021
  Place:	Zoom @ online
  16:00-17:30	Will Donovan (Tsinghua)
  “Classification of simple flops and variation of GIT”
  Though classification of flops remains very challenging in general, progress on classification of simple flops has been made by D. Li and A. Kanemitsu, focusing on their relation with Fano manifolds. Derived equivalence are conjectured for all, and remain open in many cases. I review this, and discuss approaches to proving new equivalences using variation of GIT, in joint work with Weilin Su.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory XIV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discuss first properties of schemes, beginning with open and closed immersions.

• Date:	Wed 27th Jan, 2021
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory XIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue discuss first properties of schemes, beginning with those of being noetherian or locally noetherian.

• Date:	Wed 20th Jan, 2021
  Place:	Zoom @ online
  16:00-17:30	Calla Tschanz (Bath)
  “Scheme Theory XII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we discuss first properties of schemes.

• Date:	Wed 13th Jan, 2021
  Place:	Zoom @ online
  16:00-17:30	Harry Rainbird (Bath)
  “Scheme Theory XI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme beginning by considering the functor from varieties to schemes.

• Date:	Wed 16th Dec, 2020
  Place:	Zoom @ online
  16:00-17:30	Oscar Finegan (Cardiff)
  “Scheme Theory X”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme beginning with the proof that Proj of a graded ring is a scheme.

• Date:	Wed 9th Dec, 2020
  Place:	Zoom @ online
  16:00-17:30	Alan Thompson (Loughborough)
  “Mirror symmetry for fibrations and degenerations”
  In a 2004 paper, Tyurin briefly hinted at a novel relationship between Calabi-Yau mirror symmetry and the Fano-LG correspondence. More specifically, if one can degenerate a Calabi-Yau manifold to a pair of (quasi-)Fanos, then one expects to be able to express the mirror Calabi-Yau in terms of the corresponding Landau-Ginzburg models. Some details of this correspondence were worked out by C. F. Doran, A. Harder, and I in a 2017 paper, but much remains mysterious. In this talk I will describe recent attempts to better understand this picture, and how it hints at a broader mirror symmetric correspondence between degeneration and fibration structures. As an example of this correspondence, I will discuss the question of finding mirrors to certain exact sequences which describe the Hodge theory of degenerations. The material in this talk is joint work in progress with C. F. Doran.
  17:30-18:15	Oscar Finegan (Cardiff)
  “Scheme Theory IX”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme beginning with the Proj construction.

• Date:	Wed 2nd Dec, 2020
  Place:	Zoom @ online
  16:00-17:30	Harkaran Uppal (Bath)
  “Scheme Theory VIII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme beginning with its formal definition.

• Date:	Wed 25th Nov, 2020
  Place:	Zoom @ online
  16:00-17:30	Agnieszka Bodzenta-Skibinska (Warsaw)
  “Exact categories and abelian envelopes” Video recording available (YouTube)
  For exact categories I will develop a theory parallel to the theory well-known for triangulated categories; left and right admissible subcategories, and (semi-orthogonal) decompositions. In particular, I will introduce thin exact categories, i.e. exact categories will full exceptional collections. I will discuss left and right abelian envelopes of an exact category and will show that highest weight categories are precisely the abelian envelopes of thin exact categories. I will also discuss Ringel duality from this point of view. This is a joint work with A. Bondal.
  17:30-18:15	Calla Tschanz (Bath)
  “Scheme Theory VII”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme beginning with the functoriality of the Spec construction.

• Date:	Wed 18th Nov, 2020
  Place:	Zoom @ online
  16:00-17:30	Wing Kei Poon (Bath)
  “Scheme Theory VI”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme and the basic properties of the structure sheaf of the spectrum of a ring.

• Date:	Wed 11th Nov, 2020
  Place:	Zoom @ online
  16:00-17:30	Daria Polyakova (Copenhagen)
  “Weakly monoidal structure for the DG-category of representations up to homotopy”
  Representations up to homotopy of a group G were introduced by Abad and Crainic. They form a DG-category Rep^h(G) whose objects are A-infinity comodules over the coalgebra of functions on G, and whose morphisms are A-infinity Hom complexes. This category enhances the derived category of ordinary representations. Abad-Crainic-Dherin proved that the homotopy category of Rep^h(G) is monoidal. They posed a question to define an appropriate homotopy-coherent structure on the DG-category itself.I will explain how a family of polytopes controls morphisms of A-infinity (co)modules. Then I will present a new observation that this family is nothing else but freehedra, a family constructed earlier by Saneblidze for entirely different reasons as subdivisions of cubes. Abad-Crainic-Dherin monoidal structure appears to follow from Saneblidze’s diagonal for freehedra. I will extend this diagonal to A-infinity coalgebra structure. This is the first ingredient of a “weakly monoidal” structure that I obtain as a DG-lift of Abad-Crainic-Dherin monoidal structure.
  17:30-18:15	Chris Seaman (Cardiff)
  “Scheme Theory V”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss the notion of a scheme, beginning with basic properties of the structure sheaf of the spectrum of a ring.

• Date:	Wed 4th Nov, 2020
  Place:	Zoom @ online
  16:00-18:00	Oscar Finegan (Cardiff)
  “Scheme theory IV”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we discuss the notion of a scheme, beginning with the definition of the spectrum of a commutative ring.

• Date:	Wed 28th Oct, 2020
  Place:	Zoom @ online
  16:00-17:30	Alastair Craw (Bath)
  “Gale duality and the linearisation map for quiver moduli”
  The goal of the talk is to show you a beautiful matrix and then to explain its geometric significance. This will enable me to explain why two rival geometric interpretations of `Reid's recipe' are equivalent. To begin, I'll set the scene by discussing the classical McKay correspondence in dimension two and I'll go on to discuss how this extends naturally to dimension three. I'll introduce Reid's recipe by studying the cyclic quotient singularity of type 1/19(1,3,15), and this gives me the excuse to introduce the matrix that I've fallen in love with. I'll reveal the geometry that this gorgeous matrix encodes, and as a result, we'll see that two conjectures for consistent dimer model algebras are equivalent.
  17:30-18:15	Timothy Logvinenko (Cardiff)
  “Scheme theory III”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss sheaves of abelian groups on a topological space, beginning with short exact sequences of sheaves.

• Date:	Wed 21st Oct, 2020
  Place:	Zoom @ online
  16:00-18:00	Chris Seaman (Cardiff)
  “Scheme theory II”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we continue to discuss sheaves of abelian groups on a topological space, beginning with the kernel, image, and cokernel constructions.

• Date:	Wed 14th Oct, 2020
  Place:	Zoom @ online
  16:00-18:00	Oscar Finegan (Cardiff)
  “Scheme theory I”
  The wheel of time turns, and academic years come and pass, leaving traditions which become legend. In this series of talks we will work our way through the Chapter 2 of Hartshorne's “Algebraic geometry”, covering the basics of scheme theory. In this talk, we discuss sheaves of abelian groups on a topological space.

• Date:	Wed 12th Feb, 2020
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Chris Seaman (Cardiff)
  “Combinatorial constructions of derived equivalences II”
  In the first part of this talk, we stated the main theorem of the paper by Halpern-Leistner and Sam (Theorem 3.2 in arXiv:1601.02030). In the second part, we will briefly restate (the motivation for) this theorem, and go on to show that it constructs window-shift equivalences between the derived categories of some variations of the GIT quotient X^{ss}/G, where X is a quasi-symmetric representation of a reductive group G.

• Date:	Wed 5th Feb, 2020
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Clemens Koppensteiner (Oxford)
  “What is a holonomic log D-module?”
  We will discuss how to generalize the theory of D-modules to logarithmic geometry and in particular how to define the notion of holonomicity in this context. We will see that this is not entirely trivial, and how to obtain a satisfactory theory anyways. This is joint work with Mattia Talpo. No knowledge of D-modules or logarithmic geometry will be assumed.

• Date:	Wed 29th Jan, 2020
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Christopher Seaman (Cardiff)
  “Combinatorial constructions of derived equivalences I”
  We give a brief introduction to the results of the eponymous paper of Dan Halpern-Leistner and Steven Sam (arXiv:1601.02030) which constructs window-shift equivalences between the derived categories of the variations of a GIT quotient.

• Date:	Wed 30th Oct, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “Homogeneous spaces and Bruhat decomposition II”
  Last week we have introduced algebraic groups, their Borel and parabolic subgroups, and the homogeneous spaces G/P obtained as a factor of an algebraic group G by a parabolic subgroup P. We've also worked explicitly through the example of G = SL_2 to conclude that the corresponding space G/B is the projective space P^1. This week we will define the Bruhat decomposition G = BWB induced by the choice of a Borel subgroup B and a maximal torus T ⊂ B. We will then work though the example of G = SL_3.

• Date:	Wed 23rd Oct, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “Homogeneous spaces and Bruhat decomposition I”
  I will give a beginner-friendly introduction to the geometry of homogeneous spaces G/P via Bruhat decomposition and Schubert calculus. The main focus is on the case G = SL_n, when these homogeneous spaces are projective spaces, Grassmanians, and flag varieties. There will be explicit worked examples for G = SL_3.

• Date:	Wed 9th Oct, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “The Grothendieck–Springer resolution III”
  In this talk, we define the nilpotent cone and the Springer resolution of a complex connected Lie group. We then define the homogeneous space G/B, and identify the Springer resolution with the cotangent bundle T^∗ G/B.

• Date:	Fri 5th Oct, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Victor Przyjalkowski (HSE/Steklov)
  “On the mirror P=W conjecture”
  We discuss Katzarkov-Kontsevich-Pantev conjectures which relate Hodge numbers of Fano varieties with Hodge-type numbers of their Landau-Ginzburg models. We give their proofs in dimensions 2 and 3. We also discuss the mirror P=W conjecture which claims a deeper relation between mixed Hodge structures of log Calabi-Yau varieties and perverse Leray filtrations of Landau-Ginzburg models.

• Date:	Wed 31st Jul, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Christopher Seaman (Cardiff)
  “Classification of Finite Semi-Simple Lie Algebras II”
  Having shown last time that root systems can be classified by their associated Dynkin diagrams, we finish off the classification of finite semi-simple Lie algebras by using a theorem of Serre.

• Date:	Wed 31st Jul, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Christopher Seaman (Cardiff)
  “Classification of Finite Semi-Simple Lie Algebras I”
  In this talk we will remind ourselves of the definitions of root systems and the Weyl group, then show that irreducible root systems are classified by their associated Dynkin diagrams. This allows us to classify the finite semi-simple Lie algebras.

• Date:	Wed 24th Jul, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “The Grothendieck–Springer resolution II”
  In today's talk we will remind the basic definitions of Lie algebras and we will discuss some properties of solvable and semisimple Lie algebras.

• Date:	Wed 3rd Jul, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “The Grothendieck–Springer resolution I”
  In today's talk we will remind the basic definitions of Lie algebras, we will discuss some properties of nilpotent elements and we will give the contruction of the Springer resolution of the nilpotent cone.

• Date:	Wed 26th Jun, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “P^n-functors V”
  I will explain the new notion of (non-split) P^n-functors introduced recently in the eponymous preprint (arXiv:1905.05740). I will explain the background, define a P^n-structure on an enhanced functor, construct the induced P-twist, and give an outline of the proof that this P-twist is an autoequivalence of the target category. Then I will explain the strong monad condition. Finally, I will give some examples of non-split P^n-functors.

• Date:	Wed 12th Jun, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “P^n-functors IV”
  I will explain the new notion of (non-split) P^n-functors introduced recently in the eponymous preprint (arXiv:1905.05740). I will explain the background, define a P^n-structure on an enhanced functor, construct the induced P-twist, and give an outline of the proof that this P-twist is an autoequivalence of the target category. Then I will explain the strong monad condition. Finally, I will give some examples of non-split P^n-functors.

• Date:	Wed 5th Jun, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “P^n-functors III”
  I will explain the new notion of (non-split) P^n-functors introduced recently in the eponymous preprint (arXiv:1905.05740). I will explain the background, define a P^n-structure on an enhanced functor, construct the induced P-twist, and give an outline of the proof that this P-twist is an autoequivalence of the target category. Then I will explain the strong monad condition. Finally, I will give some examples of non-split P^n-functors.

• Date:	Fri 31st May, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “P^n-functors II”
  I will explain the new notion of (non-split) P^n-functors introduced recently in the eponymous preprint (arXiv:1905.05740). I will explain the background, define a P^n-structure on an enhanced functor, construct the induced P-twist, and give an outline of the proof that this P-twist is an autoequivalence of the target category. Then I will explain the strong monad condition. Finally, I will give some examples of non-split P^n-functors.

• Date:	Wed 22nd May, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Timothy Logvinenko (Cardiff)
  “P^n-functors”
  I will explain the new notion of (non-split) P^n-functors introduced recently in the eponymous preprint (arXiv:1905.05740). I will explain the background, define a P^n-structure on an enhanced functor, construct the induced P-twist, and give an outline of the proof that this P-twist is an autoequivalence of the target category. Then I will explain the strong monad condition. Finally, I will give some examples of non-split P^n-functors.

• Date:	Wed 15th May, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Chris Seaman (Cardiff)
  “Perverse schobers”
  The group of autoequivalences of a given derived category of coherent sheaves on a variety X, D^b(X), has been the subject of much study. In this talk I will present some well-known results about Aut(D^b(X)), as well as more recent technology in the form of perverse schobers. These should be thought of as categorifications of perverse sheaves, a way of thinking which can be made more precise through results of Bondal, Kapranov and Schechtman.

• Date:	Wed 8th May, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Daria Poliakova (Copenhagen)
  “Homotopy limits in DG categories and applications to derived algebraic geometry”
  I will explain a construction of Reedy-fibrant replacements for simplicial DG-categories with respect to Dwyer-Kan model structure. This allows for explicit formulas for homotopy limits (due to Block-Holstein-Wei and Arkhipov-Ørsted). As an application, I will demonstrate a computation of homotopy limit of a cosimplicial DG-algebra associated to a commutative Hopf DG-algebra and compare it to the classical cobar construction.

• Date:	Wed 10th Apr, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “Generalised braid actions”
  In this talk, after giving some background on autoequivalences of derived categories of smooth projective varieties, I will define the generalised braid category and describe its action on the derived categories of (the cotangent bundles of) full and partial flag varieties. Generalised braids are the braids whose strands are allowed to touch in a certain way. The basic building blocks of their action on flag varieties are spherical and non-split P- functors together with the twist equivalences they induce. I will describe our present progress and future expectations. This is a joint project with Rina Anno and Timothy Logvinenko.

• Date:	Wed 27th Mar, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “A quick tour of deformation theory II”
  Following the discussion of last'week, we will go through the definition of complex space and through the completeness, versality and universality properties of deformations.

• Date:	Wed 20th Mar, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “A quick tour of deformation theory”
  After recalling the basic definitions of deformation families, we will discuss the Kodaira-Spencer criterion for completeness and the Kuranishi Theorem on the existence of a versal deformation for every compact complex manifold.

• Date:	Wed 13th Mar, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo De Biase (Cardiff)
  “Bondal-Orlov criteria for derived equivalences V”
  We will give a brief introduction to deformation families and Kodaira-Spencer maps.

• Date:	Wed 6th Mar, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Chris Seaman (Cardiff)
  “Bondal-Orlov criteria for derived equivalences IV”
  We shall look at a lemma by Bridgeland which states that if we have a flat map S → X and an object E ∈ D(S) such that for every closed point x ∈ X the object ι_x^* E ∈ D(S_x) is a sheaf, then E itself is a sheaf on S flat over X.

• Date:	Wed 27th Feb, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Chris Seaman (Cardiff)
  “Bondal-Orlov criteria for derived equivalences III”
  Following on from the overview given two weeks ago, we shall present the spectral sequence argument which ensures that the Fourier-Mukai kernel of LF ∈ D(X × X) is a sheaf supported on Δ ⊂ X × X and flat over the projections to X.

• Date:	Wed 20th Feb, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Chris Seaman (Cardiff)
  “Bondal-Orlov criteria for derived equivalences II”
  Following on from the overview given two weeks ago, we shall begin the process of fleshing out the full details of the proof of the Bondal-Orlov criterion for a Fourier-Mukai transform to be fully faithful.

• Date:	Fri 15th Feb, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  13:10-14:10	Enrico Fatighenti (Loughborough)
  “On technical aspects of constructing Fano varieties of K3 type and IHS manifolds”
  Subvarieties of Grassmannians (and especially Fano varieties) obtained from section of homogeneous vector bundles are far from being classified. A case of particular interest is given by the Fano varieties of K3 type, for their deep links with hyperk\"ahler geometry. This talk will be mainly devoted to the construction of some new examples of such varieties. This is a work in progress with Giovanni Mongardi.

• Date:	Wed 6th Feb, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:10-18:00	Timothy Logvinenko (Cardiff)
  “Bondal-Orlov criteria for derived equivalences I”
  I will give a bird's eye overview of the well-known criterion by Bondal and Orlov for the Fourier-Mukai transform defined by a kernel F ∈ D(X × Y) to be fully faithful. We will look at the kernel composition LF ∈ D(X × X) and the successive steps through which it is established to be the structure sheaf of the diagonal Δ ⊂ X × X.

• Date:	Wed 30th Jan, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:10-18:00	Lorenzo de Biase (Cardiff)
  “Derived Equivalence vs Birationality III”
  We will continue the proof of Kawamata's result on the implication of K-equivalence from D-equivalence under the hypothesis of maximality of the (anti-canonical) Kodaira dimension.

• Date:	Wed 23rd January, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:10-18:00	Christopher Seaman (Cardiff)
  “ Derived Equivalence vs Birationality II”
  Carrying on from our digression last week, we shall remind ourselves of the statement of Kawamata's result and continue the proof. Time permitting, we shall address some corollaries of the result.

• Date:	Wed 16th January, 2019
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:10-18:00	Christopher Seaman (Cardiff)
  “Derived Equivalence vs Birationality I”
  We shall state and prove the result by Kawamata that if two smooth projective varieties are derived equivalent and the Kodaira dimension of the (anti-)canonical divisor is maximal, then the varieties are birational.

• Date:	Wed 12th December, 2018
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:10-18:00	Timothy Logvinenko (Cardiff)
  “Nefness and birationality under derived equivalence”
  We will state and prove the famous results of Kawamata on the preservation of the nefness of the canonical bundle and the preservation of the birational class under derived equivalences.

• Date:	Wed 28th November, 2018
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo de Biase (Cardiff)
  “Geometrical aspects of the Fourier-Mukai kernel”
  What happens if a Fourier-Mukai kernel $K \in D^b(XxY)$ has support not the whole product XxY but just a subvariety Z? In today's seminar we will prove some results about Supp(K): beyond their intrinsic importance, they will be the technical background for proving Kawamata's theorems on the preservation of the nefness of the canonical bundle and of the numerical Kodaira dimension under derived equivalences.

• Date:	Wed 21th November, 2018
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Christopher Seaman (Cardiff)
  “Hochschild (co)homology and geometrical aspects of the Fourier-Mukai kernel”
  After reminding ourselves of the definitions, we will study isomorphisms of Hochschild (co)homologies induced by equivalences of derived categories. Time permitting, we will explore some results on the support of the Fourier-Mukai kernel of an equivalence.

• Date:	Wed 31st October, 2018
  Place:	Room M/2.06 @ School of Mathematics, Cardiff University
  16:00-18:00	Lorenzo de Biase (Cardiff)
  “Kodaira dimension under derived equivalence”
  We will prove Orlov's result on preservation of Kodaira dimension and canonical ring under derived equivalences for smooth projective varieties. Then, we will extend the result to Hochschild cohomologies and we will recover the Hochschild-Kostant-Rosemberg isomorphism.