## Triangulated categories of log-motives over a field – Federico Binda (Università di Milano Statale)

In this talk, I will give an overview of the construction of a triangulated category of motives for log smooth log schemes over a field $k$, based on the notion of finite log correspondence, in analogy to Voevodsky’s $\mathsf{DM}(k)$. The affine…

TBA…

## Decomposition along a non-linear flag – Gabriele Vezzosi (Università di Firenze)

We define a non-commutative version of the punctured formal neighborhood in algebraic geometry, and apply this construction to give decompositions of the (derived) stacks $\mathbf{Coh}^-(X)$, $\mathbf{Perf}(X)$, and $\mathbf{Bun}_G(X)$ along a…

## Canonical liftings and log structures – Piotr Achinger (Instytut Matematyczny PAN)

In the context of mirror symmetry, the moduli space of complex Calabi-Yau varieties acquires canonical local coordinates near a “large complex structure limit point”. In characteristic p geometry, the formal deformation space of an ordinary…

## Vafa-Witten formulas and generalizations – Lothar Göttsche (ICTP, Trieste)

25 years ago Vafa and Witten predicted generating functions for the Euler numbers of the moduli spaces of sheaves on algebraic surfaces. In this talk, I review joint work with Martijn Kool to interpret and check these predictions in terms of virtual…

## On the motive of zero-dimensional Quot schemes on a curve – Barbara Fantechi (SISSA, Trieste)

This is a report on joint work with Bagnarol and Perroni, available at arxiv:1907.00826. For any locally free coherent sheaf on a fixed smooth projective curve, we study the class, in the Grothendieck ring of varieties, of the Quot scheme that…

## Smoothing of a reducible $I$-surface – Sönke Rollenske (Philipps-Universität Marburg)

The moduli space of stable surfaces is a modular compactification of the Gieseker moduli space of (canonical models of) surfaces of general type but has components consisting solely of non-smoothable surfaces. I will construct a smoothing of a…

## Constructing $T$-singular surfaces – Julie Rana (Lawrence University)

Semi-log-canonical surfaces with ample canonical divisors are called stable. Their moduli space is a natural compactification (the KSBA compactification) of the Gieseker moduli space of canonical models of surfaces of general type. Among the…

## Crystalline fundamental group and Berthelot’s conjecture for isocrystals – Fabio Tonini (Università di Firenze)

In the talk I will introduce the crystalline site of a variety in positive characteristic, discuss the notion of crystals and isocrystals over it and define its crystalline fundamental group. I will then discuss Berthelot’s conjecture and its…

## The universal affine extension of an abelian variety – Michel Brion (Université Grenoble Alpes)

Every abelian variety $A$ over a field $k$ admits a universal extension by an affine $k$-group scheme. The talk will present a construction of this universal affine extension (first due to Serre when $k$ is algebraically closed of characteristic…

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