## Two results about Grothendieck’s Section Conjecture – Giulio Bresciani (SNS Pisa)

Grothendieck’s Section Conjecture states that, if $X$ is an hyperbolic curve over a field $k$ finitely generated over $\mathbb{Q}$, every section of the map $\pi_1(X) \to \mathsf{Gal}(k)$ is associated with a rational point of the completion of $X$.…

## Boundary divisors in the stable pair compactification of the moduli space of Horikawa surfaces – Luca Schaffler (Roma 3)

Smooth minimal surfaces of general type with $K^2=1$, $p_g=2$, and $q=0$ constitute a fundamental example in the geography of algebraic surfaces, and the 28-dimensional moduli space $M$ of their canonical models admits a geometric and modular…

## Parabolicity conjecture of F-isocrystals – Marco D’Addezio (Université de Paris)

In the last years the theory of crystalline cohomology and F-isocrystals had a great development. I will present a new result concerning the algebraic monodromy groups of F-isocrystals. I will start with a quick introduction on crystalline…

## Variation of stable birational type and bounds for complete intersections – Johannes Nicaise (KU Leuven and Imperial College London)

This talk is based on joint work with John Christian Ottem. I will explain a generalization of results by Shinder on variation of stable birational types in degenerating families, and how this can be used to extend Schreieder’s non-stable…

## Local positivity and effective Diophantine approximation – Matthias Nickel (Pisa)

In this talk I will discuss a new approach to prove effective results in Diophantine approximation relying on lower bounds of Seshadri constants. I will then show how to use it to prove an effective theorem on the simultaneous approximation of two…

## 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…

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