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# Categoria evento: Algebraic and Arithmetic Geometry Seminar

## TBA – Francesca Carocci (Université de Genève)

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## TBA – Souvik Goswami (University of Barcelona)

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## The J-invariant of linear algebraic groups of outer type – Nikita Geldhauser (LMU Munich)

The J-invariant is a discrete invariant of semisimplealgebraic groups which describes the motivic behavior of the variety ofBorel subgroups. This invariant was an important tool to solve severallong-standing problems. For example, it plays an…

## On Moduli of Quiver Representations and Applications to Geometry – Patricio Gallardo (University of California, Riverside)

The moduli of quiver representations, i.e. tuples of line maps arranged per a prescribed directed graph, serve as a key tool within geometry and representation theory. In this talk, we will describe their structure and explore their applications to…

## Why Markman saves the Hodge conjecture for Weil type cycles from Kontsevich (in dimension 4) – Patrick Brosnan (University of Maryland)

I’ll explain two opposing pieces of work: (1) Markman’s proof of theHodge conjecture for general Weil type abelian fourfolds of discriminant 1, and (2) Kontsevich’s tropical approach to finding a counterexample to the Hodgeconjecture for Weil type…

## Hodge-to-singular correspondence – Mirko Mauri (IST Austria)

We show that the cohomology of moduli spaces of Higgs bundles decomposes in elementary summands depending on the topology of the symplectic singularities on a (fixed!) master object and/or the combinatorics of certain posets and lattice polytopes.…

## (Non-archimedean) SYZ fibrations for Calabi-Yau hypersurfaces – Enrica Mazzon (University of Regensburg)

The SYZ conjecture is a conjectural geometric explanation of mirror symmetry. Based on this, Kontsevich and Soibelman proposed a non-archimedean approach, which led to the construction of non-archimedean SYZ fibrations by Nicaise-Xu-Yu. A recent…

## Diophantine methods and S-unit equations – Samuel Le Fourn (Institut Fourier, Grenoble)

Baker’s method (based on linear forms in logarithms) and Runge’s method (based on the pigeonhole principle) both allow to bound heights of integral points on curves (or even varieties) in certain situations which turn out to be rather different. In…

## More efficient algorithms using stack-theoretic weighted blow-ups – David Rydh (Stockholm)

Abramovich, Temkin and Wlodarczyk has recently given an easier and more efficient algorithm for resolution of singularities using stack-theoretic weighted blow-ups. Weighted blow-ups generalize root stacks and ordinary blow-ups but are far more…