## Upcoming conferences & activities

## Geometric Representation Theory

## Twinned conference "Geometric Representation Theory", June 22 - 26, 2020

This will be a twinned conference held simultaneously at Max Planck Institute in Bonn, Germany and Perimeter Institute in Waterloo, Canada. The two venues will be connected by live video streams, during both the talks themselves as well as informal discussion sessions.

## 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.

## Some adjoint L-values and Hilbert modular Eisenstein congruences

I will start from the situation of a cuspidal Hecke eigenform f of real quadratic character, congruent to its complex conjugate modulo a prime P ramified in the coefficient field.

## The m-step solvable anabelian geometry of finitely generated fields

A celebrated theorem of Neukirch and Uchida states that two number fields are isomorphic if their absolute Galois groups are isomorphic. The Grothendieck birational conjecture predicts a similar result for all finitely generated fields. This has been proved by Pop, using in an essential way the Neukirch-Uchida theorem for global fields.

## -- Cancelled -- Powers of the Dedekind eta function and the Bessenrodt-Ono inequality

In this talk I present recent results obtained with Markus Neuhauser towards the non-vanishing of the coefficients of the Dedekind eta function in the spirit of G.-C. Rota. This includes Serre’s table, pentagonal numbers, results of Kostant in the context of simple affine Lie algebras and the Lehmer conjecture. In the second part I will talk about partition numbers and the Bessenrodt-Ono inequality.

## IMPRS seminar on various topics: Period domains

## Local behaviour of the set of the values of Euler's totient function

Let $V$ be the set of the values of the Euler's $\varphi$ function. It is known that the natural density of $V$, namely the limit of $V(x)/x$, as $x$ tends to infinity, is $0$.

In a paper to appear, M. K. Das, P. Eyyunni and B. R. Patil claim that this also applies to a local density of $V$, known as the uniform upper density, or the Banach density, defined by

$$

\delta^{*(}V) = \lim_{H \rightarrow \infty} \limsup_{x \rightarrow \infty} \frac{1}{H}\left(V(x+H) -V(x)\right).

$$

## Higgs bundles on Riemann surfaces, II

On a Riemann Surface $\Sigma$, the moduli space of polystable $\mathrm{SL}_n(\mathbb{C}$)-Higgs bundles can be identified with the space of reductive representations $\pi _1 (\Sigma) \to \mathrm{SL}_n(\mathbb{C})$. In this talk, we discuss a proof of this so called non-abelian Hodge correspondence. Our goal is to understand how

to construct a Higgs bundle from a given representation and how this construction relates to the theory of harmonic maps.

## Lower Bounds for Discrete Negative Moments of the Riemann zeta Function

I will talk about lower bounds for the discrete negative 2k-th moment of the derivative of the Riemann zeta function for all

fractional k > 0. The bounds are in line with a conjecture of Gonek and Hejhal. This is a joint work with Winston Heap and

Junxian Li.

## Coxeter Groups

## 1. Singular Hodge theory of matroids; 2. Logarithmic concavity of weight multiplicities for irreducible sln(C)-representations

Talk 1: Title: Singular Hodge theory of matroids

If you take a collection of planes in R

3, then the number of lines you get by intersecting the planes is at least the number of planes. This is an example of a more general statement, called the “Top-Heavy Conjecture”, that Dowling and Wilson conjectured in 1974.On the other hand, given a hyperplane arrangement, I will explain how to uniquely associate a certain polynomial (called its Kazhdan–Lusztig polynomial) to it.

## 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 seminar on various topics: Hitchin systems

## IMPRS Minicourse

## Representation theory learning seminar

## Extra talk

## 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

## Twinned conference "Geometric Representation Theory", June 22 - 26, 2020

This will be a twinned conference held simultaneously at Max Planck Institute in Bonn, Germany and Perimeter Institute in Waterloo, Canada. The two venues will be connected by live video streams, during both the talks themselves as well as informal discussion sessions.

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## Reading group on geometric group theory

## Reading group on geometric group theory

## Reading group on geometric group theory

## Reading group on geometric group theory

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