## On the canonical, fpqc, and finite topologies: the state of the art – Luisa Fiorot (Università di Padova)

This talk is based on joint work with Yves André dedicated to the study of the behaviour of finite coverings of (affine) schemes with regard to two Grothendieck topologies: the fpqc topology and the canonical topology (i.e., the finest topology for…

## Birational geometry of the intermediate Jacobian fibration – Giulia Saccà (Columbia University)

I will start by presenting some applications of the minimal model program to the construction of symplectic compactifications of certain Lagrangian fibrations (integrable systems) of geometric origin. One such case is that of the intermediate…

## Elliptic quintics on cubic fourfolds, O’Grady 10 and Lagrangian fibrations – Laura Pertusi (Università di Milano Statale)

In this talk we study certain moduli spaces of semistable objects in the Kuznetsov component of a cubic fourfold. We show that they admit a symplectic resolution $\tilde M$ which is a smooth projective hyperkaehler manifold deformation equivalent to…

## Stacks, blowing up and resolution – Dan Abramovich (Brown University)

I will describe a class of stack-theoretic modifications, and sketch how they are applied in resolution of singularities. This is a concrete exposition of work with Temkin and Wlodarczyk and of work of Quek.…

## Crystalline and étale companions – Kiran S. Kedlaya (University of California San Diego)

When studying the zeta functions of algebraic varieties over finite fields of characteristic $p$, there are essentially two approaches to put these in the context of a Weil cohomology theory. One approach is the familiar one using etale cohomology;…

## Symplectic structures on moduli of Stokes data – Tony Pantev (University of Pennsylvania)

I will discuss the notion of shifted symplectic structures along the stalks of constructible sheaves of derived stacks on stratified spaces. I will describe a general pushforward theorem producing relative symplectic forms and will explain explicit…

## The Hilbert scheme of infinite affine space – Burt Totaro (UCLA)

I will discuss the Hilbert scheme of d points in affine $n$-space, with some examples. This space has many irreducible components for $n$ at least $3$ and is poorly understood. Nonetheless, in the limit where n goes to infinity, we show that the…

## Derived invariants in characteristic $p$ – Benjamin Antieau (Northwestern University)

I will discuss joint work with Daniel Bragg on the identification of derived invariants of smooth projective varieties in characteristic $p$, especially using information from crystalline cohomology.…

## What determines a variety? – János Kollár (Princeton University)

A scheme X is a topological space — which we denote by $|X|$ — and a sheaf of rings on the open subsets of $|X|$. We study the following natural but seldom considered questions. How to read off properties of $X$ from $|X|$? Does $|X|$ alone…

## Brauer groups of moduli of hyperelliptic curves, via cohomological invariants – Roberto Pirisi (KTH Stockholm)

We use the theory of cohomological invariants for algebraic stacks to completely describe the Brauer group of the moduli stacks $H_g$ of genus $g$ hyperellitic curves over fields of characteristic zero, and the prime-to-$\mathsf{char}(k)$ part in…

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