## Freezing transition for the Riemann zeta function on a short interval

In this talk, we will present a proof of the freezing transition for the Riemann zeta function as conjectured by Fyodorov, Hiary & Keating. The connection with log-correlated fields will be emphasized. The problem is related to understanding moments of zeta on a typical short interval. The proof relies on techniques developed to understand the leading order of the maximum of zeta. If time permits, we will discuss the “one-step replica symmetry breaking behaviour” (1-RSB) which can be proved for a simplified model of zeta.

## Mini-course: Riemann zeta function and log-correlated fields, Part 2

For info, the Part 1 will take place in Lipschitz Saal, Uni Bonn (Endenicher Allee 60),

Tuesday 12th June, 9h00-10h45.

## Short talk: The Fyodorov-Bouchaud formula and Liouville conformal field theory

Starting from the restriction of a 2d Gaussian free field (GFF) to the unit circle one can define a Gaussian multiplicative chaos (GMC) measure whose density is formally given by the exponential of the GFF. In 2008 Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of this GMC. In this talk we will explain how to prove rigorously this formula by using the techniques of conformal field theory.

## Mini-course: Random matrices and logarithmically correlated fields, Part 2

For info: the Part 1 will take place in Lipschitz Saal at Uni Bonn (Endenicher Allee 60), Monday 11th June, 14h00-15h45.

## Short talk: First order asymptotic of Liouville four-point correlation function and the conformal bootstrap

Based on the rigorous path integral formulation of Liouville conformal field theory introduced by David-Kupiainen-Rhodes-Vargas, we compute the first order asymptotic of the four-point correlation function on the sphere as two insertions get close together, which is expected to describe the density of vertices around the root of large random planar maps.

## Basics of the BV formalism - Part 2

If the Batalin-Vilkovisky formalism is a cohomological handle for field theories in the Lagrangian formalism, a similar construction can be set up for the associated Hamiltonian picture and goes under the name of Batalin, Fradkin and Vilkovisky (BFV).

The link between the two has been made explicit recently by Cattaneo, Mnev and Reshetikhin (CMR) as a tool to treat field theories on manifolds with boundary.

In this talk I will review the basics of the BFV and CMR constructions and show how they relate to what we have done so far.

## The Hopf-invariant one problem and applications

## tba

## Introduction to elliptic cohomology

## p-adic dimentions

## tba

## Classical torsion and L^2-torsion I

## Construction of harmonic maps between Riemannian manifolds

By definition, harmonic maps between Riemannian manifolds are critical points of the energy functional.

In local coordinates the condition for a map to be harmonic constitutes a system of non-linear,

elliptic partial differential equations of second order.

Clearly, solutions to such differential equations are typically such maps are hard to construct.

In this talk we present a few construction methods of harmonic maps between Riemannian manifolds.

Furthermore, we will briefly explain applications of harmonic maps to other research areas (in Mathematics).

## On a non-abelian analogue of the Polya-Vinogradov inequality

We consider an analogue of the classical Polya-Vinogradov inequality for character sums in

the context of the group GL(2) over finite fields. This is joint work with Satadal Ganguly.

## On a universal Torelli theorem for elliptic surfaces

## On a universal Torelli theorem for elliptic surfaces

Given two semistable elliptic surfaces over a smooth, projective curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the N{\'e}ron-Severi lattices of the base changed elliptic surfaces for all finite separable maps $B\to C$ arises from

an isomorphism of the elliptic surfaces. Without the effectivity hypothesis, we show that the two elliptic surfaces are isomorphic.

## A universal Torelli-Tate theorem for elliptic surfaces

Given two semistable elliptic surfaces over a smooth, projective curve $C$ defined over a field of characteristic zero or finitely generated over its prime field, we show that any compatible family of effective isometries of the N{\'e}ron-Severi lattices of the base changed elliptic surfaces for all finite separable maps $B\to C$ arises from

an isomorphism of the elliptic surfaces. Without the effectivity hypothesis, we show that the two elliptic surfaces are isomorphic.

## Computation without Representation -- change of time --

A major part of "quantum topology" (you don't have to know what's that) is the definition and computation of various knot invariants by carrying out computations in quantum groups (you don't have to know what are these). Traditionally these computations are carried out "in a representation", but this is very slow: one has to use tensor powers of these representations, and the dimensions of powers grow exponentially fast.

## Braids and the Grothendieck-Teichmüller Group -- change of time --

I will explain what are associators (and why are they useful and natural) and what is the Grothendieck-Teichmüller group, and why it is completely obvious that the Grothendieck-Teichmüller group acts simply transitively on the set of all associators. Not enough will be said about how this can be used to show that "every bounded-degree associator extends", that "rational associators exist", and that "the pentagon implies the hexagon".

## An example of BV quantization in action

The purpose of this talk is to survey the machinery developed

by Costello, with an emphasis on the procedure by which one starts with

an action functional and ends up with higher algebraic structure at the

end. The running example will take as input the curved beta-gamma

system, a 2d sigma model of maps from a Riemann surface to a complex

manifold. I will sketch how to construct its BV quantization and how to

analyze its factorization algebra, which determines a sheaf of vertex

algebras known as "chiral differential operators." The talk aims to be

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