## On reduction steps for Leopoldt’s conjecture – Fabio Ferri (Università di Exeter)

Let $p$ be a rational prime and let $L/K$ be a Galois extension of number fields with Galois group $G$. Under some hypotheses, we show that Leopoldt’s conjecture at $p$ for certain proper intermediate fields of $L/K$ implies Leopoldt’s conjecture at…

## Hilbert-Kunz density function and its applications to some Hilbert-Kunz multiplicity conjectures – Vijaylaxmi Trivedi (Tata Institute of Fundamental Research, India)

In this talk we introduce a compactly supported and real valued continuous function called Hilbert-Kunz (HK) density function. We briefly describe its properties and its applications to study characteristic p-invariants like HK multiplicity and F…

## On finite presentation for the tame fundamental group – Vasudevan Srinivas (Tata Institute of Fundamental Research, India)

This is a report on joint work with H. Esnault and M. Schusterman.Recall that the étale fundamental group of a variety over an algebraically closed field of characteristic 0 is known to be a finitely presented profinite group; this is proved by…

## The Heisenberg category of a category – Ádám Gyenge (Alfréd Rényi Institute of Mathematics)

The Heisenberg algebra associated with a lattice is a much-investigated object originating in quantum theory. Khovanov introducedrecently a categorification of the infinite Heisenberg algebraassociated with the free boson or, equivalently, a rank 1…

## Hecke correspondences and Lagrangian fibrations – Sam DeHority (Columbia University)

I will discuss a method to associate new algebraic structures with deformations to certain holomorphic Lagrangian fibrations, and describe their relation with other parts of mathematical physics. This algebraic structure controls the enumerative…

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