Schedule

Tuesday 6 August 2024
All talks in Lecture Theatre A, Watson Building, University of Birmingham. (Ground floor)
Coffee breaks and lunch in the Mathematical Learning Centre, Watson Building, University of Birmingham. (First floor)

9:00 - Registration

9:30 - Rob Silversmith (Warwick)

10:30 - Coffee

11:00 - Andrew Harder (Lehigh)

12:00 - Junior Talks

12:30 - Lunch

2:00 -  Kimoi Kemboi (Princeton)

3:00 - Junior Talks

3:30 - Coffee

4:00 - Ed Segal (UCL)

Wednesday 7 August 2024
All talks in Lecture Theatre A, Watson Building, University of Birmingham. (Ground floor)
Coffee breaks and lunch in the Mathematical Learning Centre, Watson Building, University of Birmingham. (First floor)

9:30 - Junwu Tu (Shanghai)

10:30 - Coffee

11:00 - Alan Thompson (Loughborough)

12:00 - Junior Talks

12:30 - Lunch

2:00 - Elana Kalashnikov (Waterloo)

3:00 - Coffee

3:30 - Junior Talks

5:00 - Reception, and later conference dinner

Thursday 8 August 2024
All talks in Lecture Theatre A, Watson Building, University of Birmingham. (Ground floor)
Coffee breaks and lunch in the Mathematical Learning Centre, Watson Building, University of Birmingham. (First floor)

9:30 - Ailsa Keating (Cambridge)

10:30 - Coffee

11:00 - Soheyla Feyzbakhsh (Imperial)

12:00 - Lunch

2:00 - Marton Hablicsek (Leiden)

3:00 - Coffee

3:30 - Kai Hugtenburg (Lancaster)

Friday 9 August 2024
All talks in Lecture Theatre A, Watson Building, University of Birmingham. (Ground floor)
Coffee breaks and lunch in the Mathematical Learning Centre, Watson Building, University of Birmingham. (First floor)

10:00 - Renata Picciotto (Cambridge)

11:00 - Coffee

11:30 - Jeff Hicks (Edinburgh)

Titles and Abstracts

• Soheyla Feyzbakhsh (Imperial College) - Relations of Kuznetsov components of a Gushel-Mukai variety and its hyperplane sections

Let X be a very general Gushel–Mukai variety of dimension n>3, and let Y be a smooth hyperplane section. There are natural pull-back and push-forward functors between the Kuznetsov components of X and Y. In this talk, I will show that the Bridgeland stability of objects is preserved under both of these functors and discuss some applications of this result. Joint work with Henfei Guo, Zhiyu Liu and Shizhuo Zhang. 

• Marton Habicsek (Leiden University) - A formality result for logarithmic Hochschild (co)homology

Hochschild homology is a foundational invariant for associate algebras, schemes, stacks, etc. For smooth and proper varieties X over a field of characteristic 0, Hochschild homology and its variants, like cyclic homology, are closely related to Hodge cohomology and to de Rham cohomology. In this talk, via a geometric approach, we extend Hochschild homology to logarithmic schemes, in particular to compactifications, i.e, to pairs (X,D) where X is a smooth and proper variety and D is a simple normal crossing divisor. This geometric approach allows us to extend well-known facts about Hochschild homology and its variants to a logarithmic setting, in particular, (1) we generalize the celebrated HKR theorem to relate logarithmic Hochschild homology to logarithmic differential forms, (2) we define and provide a description of logarithmic cyclic homology, (3) and we compute log Hochschild (co)homology of logarithmic orbifolds. This is a joint work with Francesca Leonardi and Leo Herr.

• Andrew Harder (Lehigh University) - Tropical geometry of Clarke mirror pairs

I'll explain how to construct a graded sheaf of vector spaces on the tropicalization of any nondegenerate toric hypersurface whose cohomology recovers the orbifold Hodge numbers of the original hypersurface. This partially generalizes work of Itenberg, Katzarkov, Mikhalkin, and Zharkov. As an application, we prove that a stringy Hodge-number duality statement holds for a large and mysterious class of toric mirror pairs called Clarke mirror Landau-Ginzburg models. Using this, we recover a famous result of Batyrev and Borisov, a result of Krawitz, and prove a conjecture of Katzarkov, Kontsevich, and Pantev. Time permitting, I'll mention an unexpected relationship between certain maximally mutable Laurent polynomials and the Deligne-Hodge numbers of singular toric varieties. Joint with Sukjoo Lee (Edinburgh).

• Kai Hugtenburg (University of Lancaster) - Open Gromov-Witten invariants from the Fukaya category

Open Gromov-Witten invariants count holomorphic curves with boundary on a Lagrangian submanifold. In this talk I will explain how one can extend enumerative mirror symmetry to include open Gromov-Witten invariants, and how one can obtain open Gromov-Witten invariants from the Fukaya category, thus realising part of Kontsevich's proposal that homological mirror symmetry implies enumerative mirror symmetry.

• Alan Thompson (University of Loughborough) - Mirror symmetry for fibrations and degenerations of K3 surfaces

I will describe recent progress, joint with L. Giovenzana, on the problem of mirror symmetry for Type II degenerations of K3 surfaces. I will give a lattice-theoretic definition for when a Type II degeneration of K3 surfaces and an elliptically-fibred K3 surface, with an appropriate splitting of the base, form a mirror pair. I will then explain how this definition is compatible with lattice polarised mirror symmetry for K3 surfaces and with Fano-LG mirror symmetry for (quasi) del Pezzo surfaces. The upshot will be a concrete mirror symmetry conjecture for these objects. Finally, I will describe recent joint work with C. F. Doran and E. Pichon-Pharabod which allows this conjecture to be checked in explicit examples.

• Junwu Tu (Shanghai Tech) - B-model Categorical Enumerative Invariants and the holomorphic anomaly equations

In this talk, we shall discuss categorical enumerative invariants (CEI) associated with derived categories of coherent sheaves on smooth and projective Calabi-Yau $3$-folds. We shall sketch a proof that these B-model CEI satisfy Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation for any miniversal family of smooth projective CY $3$-folds. This provides some evidence that the B-model CEI may be taken as a definition of the B-model topological string partition function. 

• Ed Segal (University College, London) - The categorical origins of equivariant quantum cohomology

Given a Hamiltonian U(1) action on a symplectic manifold one can try to generalize the Fukaya category to a `U(1) equivariant Fukaya category'. I will describe the (2-)categorical structure that is believed to arise when we do this, and how it should be possible to recover equivariant quantum cohomology from this structure. I'll also discuss the mirror picture and show how to calculate the mirror to equivariant quantum cohomology in many examples.