## Upcoming conferences & activities

## Higher Geometric Structures along the Lower Rhine XI, March 8-9, 2018

This is the eleventh of a series of short workshops jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.

## Conference on Arithmetic and Automorphic Forms on the occasion of Günter Harder's 80th birthday, March 12 - 14, 2018

**Conference on **

**Arithmetic and Automorphic Forms **

**on the occasion of Günter Harder's 80th birthday**

**March 12 - 14, 2018**

#### Scientific Committee

Werner Ballmann, Michael Rapoport, and Joachim Schwermer

#### Local Organizer

Werner Ballmann and Christian Blohmann

#### Speakers

Kai Behrend (U British Columbia)

Spencer Bloch (U Chicago)

Gaetan Chenevier (U Paris-Sud, Orsay)

Mark Goresky (IAS Princeton)

Tasho Kaletha (U Michigan)

Stephen S. Kudla (U Toronto)

Richard Pink (ETH Zürich)

Anantharam Raghuram (IISER Pune)

Andrei Rapinchuk (U Virginia)

Peter Scholze (U Bonn)

Carlos Simpson (U Nice)

Gerard van der Geer (U Amsterdam)

## Conference "Dynamics: Topology and Numbers", July 2 - 6, 2018

**Conference "Dynamics: Topology and Numbers"**

**July 2 - 6, 2018 **

## Conference "Higher algebra and mathematical physics", August 13 - 17, 2018

**Double conference "Higher algebra and mathematical physics"**

**August 13 - 17, 2018 **

## Upcoming Talks

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

## Rational homology cobordisms of plumbed manifolds and arborescent link concordance

We investigate rational homology cobordisms of 3-manifolds with non-zero first Betti number.

This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links.

We introduce a systematic way of constructing rational homology cobordisms between plumbed 3-manifolds and concordances between arborescent links.

We then describe a sliceness obstruction based on Donaldson's diagonalization theorem that leads to a proof of the slice-ribbon conjecture for 2-component Montesinos' links up to mutation.

## Quadratic Relations in Feynman Categories

I will start with a brief introduction to Feynman categories, and then explore the consequences of

quadratic relations for the morphisms in Feynman categories.

In the first part of the talk, I show how this leads to cubical complexes and prove that in this

way both the complex for moduli spaces of curves and the cubical complexes for Cutkosky rules

and calculations for Outer space arise naturally from push-forwards.

In the second part, I study generalizations of the quadradtic relations, which naturally lead

## tba

## On Sequences of Integers of Quadratic Fields and Relations with Artin’s Primitive Root Conjecture

I will consider the integers $\alpha$ of the quadratic field $ \mathbb{Q} (\sqrt[]{d})$ with $d$ is a square-free integer. Using the embedding into $ \text{GL}(2,\mathbb{R})$ we obtain bounds for the smallest positive integer $\nu$ such that $\alpha^\nu\equiv 1\bmod p.$ More generally, if $\mathcal{O}_{f}$ is a number ring of conductor $f$, we study the first integer $n=n(f)$ such that $\alpha^n\in\mathcal{O}_{f}$. We obtain bounds for $n(f)$ and for $n(fp^{k})$.

## Doubling Properties of Solutions to Elliptic PDE

## New guests at the MPIM

## Representation theory learning seminar

## The Hilbert scheme of points of affine 3-space

We describe the scheme structure of the Hilbert scheme of points of affine 3-space,

in terms of representations of the Jacobi algebra of a quiver with potential. This exhibits the Hilbert scheme of points as the critical locus of a regular function on a smooth variety.

We discuss the torus action on the Hilbert scheme and its Euler characteristic.

## Hecke's integral formula and Kronecker's limit formula for an arbitrary extension of number fields

The classical Hecke's integral formula expresses the partial zeta function of real quadratic fields as an integral of the real analytic Eisenstein series along a certain closed geodesic on the modular curve. In this talk, we present a generalization of this formula in the case of an arbitrary extension E/F of number fields. As an application, we present the residue formula and Kronecker's limit formula for an extension E/F of number fields, which gives an integral expression of the residue and the constant term at s=1 of the``relative'' partial zeta function associated to E/F.

## On the periodicity of geodesic continued fractions

In this talk, we present some generalizations of Lagrange's periodicity theorem in the classical theory of continued fractions. The main idea is to use a geometric interpretation of the classical theory in terms of closed geodesics on the modular curve. As a result, for an extension F/F' of number fields with rank one relative unit group, we construct a geodesic multi-dimensional continued fraction algorithm to``expand'' a basis of F over the rationals, and prove its periodicity. Furthermore, we show that the periods describe the relative unit group.

## 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.

## Number theory lunch seminar

The number theory lunch seminar takes place every Wednesday after a joint lunch of MPIM's number theorists...

## IMPRS Minicourse

## Extra talk

## Seminar on Algebra, Geometry and Physics

## Seminar Algebraic Geometry (SAG)

## Higher Differential Geometry Seminar

## 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.

## Conference on "Elementare und Analytische Zahlentheorie (ELAZ)", September 3 - 7, 2018

**Conference on "Elementare und Analytische Zahlentheorie (ELAZ)"**

**September 3 - 7, 2018**

### Organizers

Kathrin Bringmann (Universität zu Köln)

Stephan Ehlen (Universität zu Köln)

Pieter Moree (MPIM Bonn)

## Conference "Higher algebra and mathematical physics", August 13 - 17, 2018

**Double conference "Higher algebra and mathematical physics"**

**August 13 - 17, 2018 **

## Conference "Dynamics: Topology and Numbers", July 2 - 6, 2018

**Conference "Dynamics: Topology and Numbers"**

**July 2 - 6, 2018 **

## Higher structures, quantum groups, and genus zero modular operad. Part 2

## Higher structures, quantum groups, and genus zero modular operad. Part 1

## What is the category of representations of classical Lie algebras of "infinite rank"?

The classical Lie algebras sl, so, sp "of infinite rank" in the naive sense have uncountably many nonconjugate Borel subalgebras. Therefore the definition of categories of their representations involves choices. A natural choice is a Dynkin Borel subalgebra. In this talk, I will advocate for another choice, namely that of a perfect Borel subalgebra. In addition, I will impose the condition of large local annihilator on the objects of the category. The resulting category is a nice highest-weight category with standard objects, but without costandard objects.