## Families of surfaces of general type

The purpose of this talk is to give a very elementary introduction to the problem of classifying surfaces of general type. I will particularly discuss the case when the surfaces are defined over an algebraically closed field of characteristic p>0, the pathologies that appear in this case in comparison to the characteristic zero case and possible ways to deal with them. The talk will be accessible to a general mathematical audience.

## Homology of the little disks operad

## Model structure on the category of operads

## Vertex Operator Algebras and Modular Forms

Time: Tuesdays, 4.30 - 6 pm

Place: MPIM Lecture Hall, Vivatsgasse 7

First lecture: on April 2, 2019, end on July 2

## Recent developments in Quantum Topology

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their

structural properties. The course is aimed to be accessible by graduate students and young researchers.

## Vertex Operator Algebras and Modular Forms

Time: Tuesdays, 4.30 - 6 pm

Place: MPIM Lecture Hall, Vivatsgasse 7

First lecture: on April 2, 2019, end on July 2

## Recent developments in Quantum Topology

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their

structural properties. The course is aimed to be accessible by graduate students and young researchers.

## Lecture course by Stavros Garoufalidis

We will review the basics of quantum topology such as the colored Jones polynomial of a knot, its standard conjectures relating to asymptotics, arithmeticity and modularity, as well as the recent quantum hyperbolic invariants of Kashaev et al, their state-integrals and their

structural properties. The course is aimed to be accessible by graduate students and young researchers.

## Vertex Operator Algebras and Modular Forms

Time: Tuesdays, 4.30 - 6 pm

Place: MPIM Lecture Hall, Vivatsgasse 7

First lecture: on April 2, 2019, end on July 2

## tba

## Arithmetic Levi-Civita Connection (after A. Buium)

The theory of arithmetic jet spaces has been developed by A. Buium using rings with a delta structure for a fixed prime p. In this arithmetic setting, the delta structure on a ring plays the analogous role of a derivative operator in geometry. One naturally associates a lift of Frobenius morphism to such a delta structure. As an example, the delta structure on the ring of integers is the Fermat quotient operator and the identity map is the associated lift of Frobenius mod p.

## Emergent Symmetries of Symmetry-Breaking Dynamic Interfaces

The (driven) Geometric Ginzburg-Landau evolution equation governs the dynamics nano-faceting crystal-melt interfaces [1]. We will provide a brief overview of the thermo-mechanics underpinning these 4th-order geometric evolution equations, which may be naturally viewed as an interpolation between crystalline mean-curvature flow and the Willmore flow. We will exhibit the emergent facet (polyhedral) dynamics that appear from these evolutions via a couple of novel geometric matched-asymptotic analysis [1,3].

## Thurston norm and L^2-Betti numbers

## Mathscamps in Africa: looking for volunteers

S.A.M.I. (Supporting African Maths Initiatives) is a UK based charity supporting the african based A.M.I. Both promotes several maths related projects, mostly (but not only) with educational purposes. Among these, one project in particular involves the organisation every year of two-weeks long maths summer camps at high-school level, ran by local mathematician volunteers, together with european mathematician volunteers, in the countries of Kenya, Ghana, Ethiopia, and this year also likely in Togo, Cameroon, Rwanda and Uganda.

## Lyapunov exponents: recent applications of Fürstenberg's theorem in spectral theory

In this talk we describe a new proof of a classical result and a number of new results that can be proved along similar lines. At the heart of this approach are the verification of the assumptions of F"urstenberg's theorem about products of random matrices and a way to parlay the output of this theorem via large deviation estimates into statements commonly referred to as ``Anderson localization.'' The various settings we consider include quantum evolution in random environments and orthogonal polynomials on the unit circle with random recursion parameters.

## New guests at the MPIM

## Linear flag ind-varieties

About two decades ago, Ivan Dimitrov and I defined ind-varieties of generalized flags. These varieties are nothing but

G/P for G=GL(infty) and a parabolic subgroup P of G. In this talk I would like to explain that the ind varieties of

generalized flags can be alternatively defined in a purely algebraic-geometric fashion as direct limits of linear

embeddings of usual flag varieties. The fact that the so-defined ind-varieties are homogeneous ind-spaces for

GL(infty) is then a consequence of the comparison theorem.

## Dimensional interpolation and the Selbergintegral (joint with D. van Straten and D. Zagier)

## Canonical Lifts in Families and delta-structures

Serre-Tate proved in the 60's that an ordinary abelian variety E over a finite field k can be canonically lifted to an ordinary abelian variety over the Witt vectors of k. Expressed in terms of the moduli stack M_ord of ordinary abelian schemes, this is precisely a universal lifting property with respect to the Witt vectors (of finite fields).

## Introduction to operads

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