Location: MB-503 at School of Mathematical Sciences, QMUL
Time: 13:00--14:00 on Tuesdays
Organisers: Wangyang Lin, Andy Xiaoan Yang
8 October (Thursday), 14:00--15:00 [One-off special date+time], MB-503
Speaker: Márton Hablicsek (Leiden)
Title: Functoriality of log Hochschild homology for log smooth pairs.
Abstract: A central question in non-commutative geometry is the existence/construction of a suitable derived category of log sheaves. Such desired derived category would have log Hochschild homology as a categorical invariant.
In my talk, I will not get closer to answer this fundamental question. However, I will provide a naive construction of a dg bicategory of log Fourier-Mukai kernels between log smooth pairs such that log Hochschild homology and cohomology are invariants of this framework. The project is joint with Ádám Gyenge and Leo Herr.
13 October, 13:00--14:00, MB-503
Speaker: Konstanze Rietsch (KCL)
Title: On mirror symmetry for Schubert varieties
Abstract: I will report on two recent works about the construction of mirror superpotentials for Schubert varieties: one with L. Williams and one with C. Li and M. Yang. The work with Williams concerns Grassmannian Schubert varieties, and generalises the Pluecker coordinate superpotential of Grassmannians using Young diagram combinatorics. The work with Li and Yang constructs a conjectural superpotential for a general G/P Schubert variety, using a completely different formulation. The two constructions are shown to produce isomorphic results in the special case. The work with Li and Yang includes a generalisation of the (Dale) Peterson variety that governs the quantum cohomology rings of the homogeneous spaces G/P, and we state a conjecture about the quantum cohomology rings of smooth Fano Schubert varieties.
20 October, 13:00--14:00, MB-503
Speaker: Joel Hakavuori (Sorbonne/IMJ-PRG)
Title: The g-theorem in smooth approximation
Abstract: The g-vector encodes the face numbers of a simplicial polytope and, by the g-theorem, is the Hilbert function of a standard graded Artinian algebra. Its entries therefore satisfy Macaulay’s growth inequalities. I will show that, along any sequence of simplicial polytopes converging in the Hausdorff metric to a convex body with C^1 boundary, the gaps from equality in the Macaulay inequalities tend to infinity. This proves a conjecture of Kalai and complements the theorem of Adiprasito, Nevo, and Samper that the nontrivial g-numbers diverge. The proof combines their construction of local affine stresses with a new lower bound for shadows of sets of monomials. Based on arXiv:2609.24790.
27 October, 13:00--14:00, MB-503
Speaker: Victoria Schleis (Durham)
Title: Symmetric realisations of simple polytopes
Abstract: Computing realizations of simple polytopes is a challenging problem. We present the implementation of a mixed symbolic-numerical algorithm that computes a realization of a simple polytope from its edge-graph. The key idea is that it is computationally more tractable to find an "as symmetric as possible" realization rather than a general one — our algorithm therefore exploits the symmetry of the face lattice to accelerate computations. We further study symmetric realizations from a theoretical perspective, examining the stratification of the realization space of a simplicial polytope according to its combinatorial symmetries.
This talk is based on joint work in progress with Daniel Longenecker (Princeton) and Charlotte Nicholas (Durham).
3 November, 13:00--14:00, MB-503
Speaker: Yizhen Zhao (QMUL)
Title: Open r-spin Theories and Categories of Matrix Factorizations
Abstract: Open r-spin theories are intersection theories on moduli spaces of holomorphic disks, while categories of matrix factorizations are algebraic structures associated to polynomials with isolated singularities. Since the moduli spaces of disks have boundary, one needs boundary conditions, and different choices have led to several open r-spin theories. I will explain how a category of matrix factorizations unifies these different choices of boundary conditions, and how open r-spin theory in turn gives cyclic A-infinity structures on this category. Based on joint work with Ran Tessler.
Past talks: 2025-2026 Sem B