Abstracts of upcoming talks at the MPIM. For an overview see also the calendar.

## New guests at the MPIM

## 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".

## Deligne categories for rational Cherednik category O

## 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.

## Introduction to elliptic cohomology

## 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.

## Gromov-Hausdorff limits of curves with flat metrics and non-Archimedean geometry

The subject of this talk is the study of the Gromov-Hausdorff limit of

a family of complex curves over a punctured disc with maximal

unipotent monodromy endowed with normalized flat metrics with conical

singularities. The limit turns out to be a metric graph which can be

naturally identified with a quotient of a subset of the Berkovich

analytic space associated to the family. This problem is inspired by

the approach of Kontsevich and Soibelman to the SYZ conjecture, and,

time permitting, I will discuss how the techniques of the talk can be

## The essential coexistence phenomenon in Hamiltonian dynamics

I will discuss a phenomenon of the essential coexistence of regular (zero Lyapunov exponents and hence, zero entropy) dynamics and chaotic (non-zero Lyapunov exponents and positive entropy) dynamics in the setting of smooth dynamical systems. I will review some recent results in this direction, discuss some open problems and describe some new examples of essential coexistence. In particular, I will outline a construction of a Hamiltonian system which demonstrate a "complete? KAM-type picture of coexistence of invariant KAM tori and surrounding "chaotic sea".

## Classical torsion and L^2-torsion I

## tba

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