## Quadratic invariants of moduli of elliptic curves – Andrea Di Lorenzo (Humboldt University)

The Chow ring of moduli of curves is an important invariant which is the subject of extensive investigations and conjectures, since Mumford first introduced the topic in his pioneering work. Chow-Witt groups are a recent refinement of the usual Chow…

## Towards a Dubrovin conjecture for Frobenius manifolds – John Alexander Cruz Morales (Universidad Nacional de Colombia & Max Planck Institute, Bonn)

In this talk we will report on ongoing work aiming to establish a Dubrovin conjecture for general Frobenius manifolds. The Dubrovin conjecture was formulated in 1998 (with a very precise statement in 2018) as a relation between the Frobenius…

## Singularities on K-moduli spaces of Fano varieties – Andrea Petracci (Università di Bologna)

Recently there has been spectacular progress, due to many scholars, on the construction of moduli (called K-moduli) of Fano varieties using K-stability (which is related to the existence of Kähler-Einstein metrics). It is a natural question to…

## Duality for motivic cohomology over local fields – Thomas Geisser (Rikkyo University)

We give an outline of a (conjectural) construction of a cohomology theory for smooth and proper varieties over local fields with values in locally compact groups, satisfying a Pontrjagin duality. For certain weights, we give an ad hoc construction…

## Abelian dynamical Galois groups – Andrea Ferraguti (SNS, Pisa)

Dynamical Galois groups are invariants associated to dynamical systems generated by the iteration of a self-rational map of $\mathbb{P}^1$. These are still very mysterious objects, and it is conjectured that abelian groups only appear in very…

## Topology of Lagrangian fibrations and $P=W$ phenomena on irreducible symplectic varieties – Camilla Felisetti (Università di Trento)

Irreducible holomorphic symplectic (IHS) varieties can be thought as a generalization of hyperkähler manifolds allowing singularities. Among them we can find for example moduli spaces of sheaves on $K3$ and abelian surfaces, which have been recently…

## The Poisson structure on the affine Grassmannian via derived algebraic geometry – Valerio Melani (Università di Pisa)

Motivated by a conjecture of Kapranov-Ginzburg-Vasserot, we will explain how to reinterpret the classical Poisson structure on the affine Grassmannian using tools from derived symplectic (and Poisson) geometry. Our approach is based on the study of…

## Archimedean height pairings for higher cycles – Gregory Pearlstein (Università di Pisa)

By the work of Richard Hain, the archimedean height pairing on ordinary algebraic cycles can be interpreted as an invariant of an associated mixed Hodge structure. In this talk, we will present a similar construction for higher cycles in the Bloch…

## From Riemann surfaces to tropical curves (and back again) – Martin Ulirsch (Goethe University Frankfurt am Main)

The surprisingly deep analogy between compact Riemann surfaces and compact metric graphs lies at the heart of many recent developments in tropical geometry. In this talk I will give a short introduction to tropical geometry via this analogy focusing…

## Surfaces with close to irrational Seshadri constants – Sönke Rollenske (Universität Marburg)

Seshadri constants measure local positivity of line bundles and it is an open question if they can be irrational on algebraic surfaces. I will recall this concept and prove that for a general point on a general hypersurface of degree $md$ in…

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