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.
Past talks: 2025-2026 Sem B