## Upcoming Talks

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

## Recent developments in Quantum Topology -- Cancelled --

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.

## Multizeta and emerging related structures in function field arithmetic

We will look at zeta, multizeta and variants taking (transcendental) values in completions of function fields rather than Artin-Weil type zeta (essentially rational functions) in characteristic zero. We discuss results and conjectures on relations they satisfy, independence results and relations to structures such as t-motives, Shtukas, absolute Galois group, Hopf algebras etc.

## Formal groups

## Mapping class groups of highly connected manifolds, I

The classical mapping class group Γ(g) of a surface of genus g shares many features with its higher dimensional analogue Γ(g,n)—the group of isotopy classes of diffeomorphisms of #ᵍ(Sⁿ x Sⁿ)—but some aspects become easier in high dimensions. This enabled Kreck in the 70’s to describe Γ(g,n) for n>2 in terms of an arithmetic group and the group of exotic spheres. His answer, however, left open two extension problems which were later understood in some dimensions, but remained unsettled in most cases.

## Mapping class groups of highly connected manifolds, II

The classical mapping class group Γ(g) of a surface of genus g shares many features with its higher dimensional analogue Γ(g,n)—the group of isotopy classes of diffeomorphisms of #ᵍ(Sⁿ x Sⁿ)—but some aspects become easier in high dimensions. This enabled Kreck in the 70’s to describe Γ(g,n) for n>2 in terms of an arithmetic group and the group of exotic spheres. His answer, however, left open two extension problems which were later understood in some dimensions, but remained unsettled in most cases.

## Lattice points, Ehrhart theory, and the relation to volumes

Continuing from the previous session, we will define the valuation for exponential sums, a discrete analogue of exponential integrals, and obtain another version of Brion's theorem. We continue to Ehrhart theory, showing polynomiality of lattice counts for polytopes with fixed cones of feasible directions. Finally, we relate exponential sums and exponential integrals via an Euler-Maclaurin type formula.

## Specializations of the Burau representation at roots of unity

The Burau representation and its specialisations at roots of unity are closely related to monodromy representations associated to families of cyclic coverings of a fixed degree of the projective line. If the number of ramifications is small relative to the degree, Deligne and Moscow constructed non arithmetic monodromy using these families. We show

## Cohomology of arithmetic groups - A specific -highly non trivial- example

## General quantization scheme for symplectic manifolds which admit Kähler structures

We will consider arbitrary holomorphic families of Kähler structures on a fixed prequantizable symplectic manifold and provided the corresponding family of Kähler quantisations for level k form a vector bundle over the chosen family of Kähler structures, we will for large enough k construct a large family of Hitchin connections in this bundle. We will also consider a natural family of Hermitian structures on the bundle of quantum spaces and understand which (unique) Hitchin connection is compatible with a given one of these Hermitian structures.

## Estimates for the Artin conductor

By using geometry of numbers, Minkowski showed that there exists a constant C such that if D_K is the discriminant of a number field K, then |D_K|>C^[K:Q]. In 1978, from the existence of infinite class field towers, Martinet constructed sequences of number fields of growing degree and bounded root discriminant.

It is natural to ask if it is possible to extends the previous results to the Artin conductor.

## Mathematical events in Bonn

##### Bonn Mathematics Calendar

All mathematical events in Bonn are listed in the Bonn Mathematics Calendar. For directions see the map.

##### University Calendar

All lectures and courses at Bonn University can be found in the university calendar.

## Recurring seminars, series and courses

Detailed list of recurring seminars, series of talks, and courses or lectures comprising multiple talks. For an overview see also the calendar.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## Reading group on "Integer points in polyhedra"

Website: https://sites.google.com/view/integerpointsonpolyhedra/home

We will introduce the algebra of (indicator functions) of polyhedra and study its properties. Linear forms on this algebra produce functions on the set of polytopes (*i.e.* bounded polyhedra), that are compatible with set-theoretic decompositions of polyhedra. For polytopes, the lattice point count or the volume are examples of such linear forms.

## IMPRS Minicourse

## Representation theory learning seminar

## Extra talk

## Seminar on Algebra, Geometry and Physics

## Archived Events

To narrow the list of events displayed please select year and event type or fill the search fields, then press *Apply*.

## MPI-Oberseminar

The Oberseminar is a very long running seminar at MPI (‘Ober‘ standing for 'upper'). Its idea is that the guests of the MPI speak in this seminar (hopefully early in their stay) and get the chance to explain their work to the other guests.

## Friedrich Hirzebruch Lecture

The annual Friedrich Hirzebruch Lecture is a series of lectures started in 2007 on the occasion of the 80th birthday of Prof. Friedrich Hirzebruch. The lectures address a general audience and aim at illustrating the relation between mathematics and art, society and other fields.

## Geometric Representation Theory

This will be a double conference held simultaneously at Perimeter Institute in Waterloo, Canada and Max Planck Institute in Bonn, Germany.

## Organizers:

Tobias Barthel, André Henriques, Joel Kamnitzer, Carl Mautner, Aaron Mazel-Gee, Kevin Mcgerty, Catharina Stroppel, Ben Webster

## tba

## Seminar "Arithmetic of Algebraic Groups"

Seminar "Arithmetic of Algebraic Groups"

## Reading group on geometric group theory

## Seminar "Arithmetic of Algebraic Groups"

Seminar "Arithmetic of Algebraic Groups"

## tba

## Reading group on geometric group theory

## Seminar "Arithmetic of Algebraic Groups"

Seminar "Arithmetic of Algebraic Groups"

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