## Quot schemes and their d-critical structure(s) – Andrea Ricolfi (SISSA, Trieste)

D-critical schemes and Artin stacks were introduced by Joyce in 2015, and play a central role in Donaldson-Thomas theory. They typically occur as truncations of (-1)-shifted symplectic derived schemes, but the problem of constructing the d-critical…

## Incontri di geometria algebrica ed aritmetica Milano – Pisa

Schedule available on: https://events.dm.unipi.it/event/109/…

## Arithmetic of homogeneous spaces over global fields of characteristic p – David Harari (Université de Paris-Saclay)

Let $K$ be the function field of a curve over a finite field. Let $X$ be a homogeneous space of a reductive group over $K$. We discuss cohomological obstructions to the local-global principle on $X$. Similar results for weak and strong approximation…

## Hilbert-Kunz density function and its applications to some Hilbert-Kunz multiplicity conjectures – Vijaylaxmi Trivedi (Tata Institute of Fundamental Research, India)

In this talk we introduce a compactly supported and real valued continuous function called Hilbert-Kunz (HK) density function. We briefly describe its properties and its applications to study characteristic p-invariants like HK multiplicity and F…

## On finite presentation for the tame fundamental group – Vasudevan Srinivas (Tata Institute of Fundamental Research, India)

This is a report on joint work with H. Esnault and M. Schusterman.Recall that the étale fundamental group of a variety over an algebraically closed field of characteristic 0 is known to be a finitely presented profinite group; this is proved by…

## The Heisenberg category of a category – Ádám Gyenge (Alfréd Rényi Institute of Mathematics)

The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introducedrecently a categorification of the infinite Heisenberg algebraassociated with the free boson or, equivalently, a rank 1…

## Hecke correspondences and Lagrangian fibrations – Sam DeHority (Columbia University)

I will discuss a method to associate new algebraic structures with deformations to certain holomorphic Lagrangian fibrations, and describe their relation with other parts of mathematical physics. This algebraic structure controls the enumerative…

## Mirror symmetry for generalized Kummer varieties – Justin Sawon (University of North Carolina at Chapel Hill, USA)

The generalized Kummer variety $K_n$ of an abelian surface $A$ is the fibre of the natural map $\mathsf{Hilb}^{n+1}A\to \mathsf{Sym}^{n+1}A\to A$. Debarre described a Lagrangian fibration on $K_n$ whose fibres are the kernels of \$\mathsf{Jac}C\to…

## Geometry of vertex operator algebras on moduli of curves – Nicola Tarasca (Virginia Commonwealth University)

The physically-inspired theory of conformal blocks allows one to construct vector bundles on moduli spaces of curves with remarkable geometric and combinatorial properties. This theory uses as input the representations of some non-commutative…

## Searching for the impossible Azumaya algebra – Siddharth Mathur (Orsay)

In two 1968 seminars, Grothendieck used the framework of etale cohomology to extend the definition of the Brauer group to all schemes. Over a field, the objects admit a well-known algebro-geometric description: they are represented by…

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