## Upcoming conferences & activities

## Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry

## Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry, June 27 - 30, 2022

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration. The concept of the twinned conference was motivated by the desire to reduce environmental impact of conference travels. Our hope is that this initiative will help reduce transatlantic flights, while still promoting long distance interactions. The goal of this twinned conference is to bring together experts on Homotopy Theory and adjacent areas to discuss the forefront of current developments in this highly active field.

We especially welcome applications from members of minority groups.

## A conference on Algebraic Topology, in memory of Hans-Joachim Baues

## A conference on Algebraic Topology, in memory of Hans-Joachim Baues

This conference is intended to provide an overview of current research in homotopy theory, which has vastly expanded since its roots in the 19th century from the study of topological spaces by algebraic and combinatorial means to other fields of mathematics, including algebraic geometry, differential topology, and mathematical physics.

## 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.

## Short lectures by new IMPRS students:

For zoom details contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

## Introduction to Fukaya categories

For zoom details please contact T. Barthel, V. Ozornova, A. Ray, P. Teichner.

## The double suspension theorem III

Abstract:

## Pressure metric in the space of Riemannian metrics

https://hu-berlin.zoom.us/j/61686623112

Contact: Gaetan Borot

## Distinguishing Siegel eigenforms from Hecke eigenvalues

Determination of modular forms is one of the fundamental and interesting

problems in number theory. It is known that if the Hecke eigenvalues of two

newforms agree for all but finitely many primes, then both the forms are

the same. In other words, the set of Hecke eigenvalues at primes determine

the newform uniquely and this result is known as the multiplicity one

theorem. In the case of Siegel cuspidal eigenforms of degree two, the

multiplicity one theorem has been proved only recently in 2018 by Schmidt.

## A Fourier transform for Banach-Colmez spaces, II

For zoom details please contact Peter Scholze (scholze@mpim...).

## Hall algebras and quantum cluster algebras

The theory of Hall algebras has known many spectacular developments and applications since the discovery by Ringel of their connection with quantum groups. One important object arising naturally in the study of Hall algebras is the integration map defined by Reineke, which allows to produce certain celebrated wall-crossing identities. In this talk I will first focus on the Dynkin case and show how the integration map can be interpreted in a natural way via the representation theory of quantum affine algebras.

## tba

Meeting-ID: 973 8400 7043

For password please contact Stephan Stadler (stadler@mpim-bonn.mpg.de).

## Miniseries on symplectic topology, Talk 2

For zoom details please contact T. Barthel, V. Ozornova, A. Ray, P. Teichner.

## 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.

## Representation theory learning seminar

## IMPRS Minicourse

## A study group on Milnor invariants

## IMPRS seminar on various topics: Hitchin systems

## 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.

## A conference on Algebraic Topology, in memory of Hans-Joachim Baues

## A conference on Algebraic Topology, in memory of Hans-Joachim Baues

This conference is intended to provide an overview of current research in homotopy theory, which has vastly expanded since its roots in the 19th century from the study of topological spaces by algebraic and combinatorial means to other fields of mathematics, including algebraic geometry, differential topology, and mathematical physics.

## Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry

## Twinned Conference on Homotopy Theory with Applications to Arithmetic and Geometry, June 27 - 30, 2022

The field of homotopy theory originated in the study of topological spaces up to deformation, but has since been applied effectively in several other disciplines. Indeed, homotopical ideas lead to the resolution of several long-standing open conjectures, for instance on smooth structures on spheres, the moduli of curves, and the cohomology of fields. More recently, Bhatt, Morrow, and Scholze used homotopical methods to compare different cohomology theories for algebraic varieties, thereby resolving open questions in arithmetic geometry. In a similarly arithmetic vein, Galatius and Venkatesh initiated the study of Galois representations with homotopical means, whereas Clausen and Scholze revisited the foundations of analytic topology. These and other recent developments in the interface of arithmetic and topology opened up new lines of attack towards classical open questions, which sparked a wide range of current research activities. This conference intends to survey some of the most spectacular recent advances in the fields, thereby paving the way to new developments and future interactions. Our goal is to foster scientific exchange and collaboration between established researchers, emerging leaders, early career mathematicians, and graduate students.

This will be a split transatlantic conference taking place at the Fields Institute in Canada and the Max Planck Institute for Mathematics in Germany, with videoconferencing connections in place to help collaboration. The concept of the twinned conference was motivated by the desire to reduce environmental impact of conference travels. Our hope is that this initiative will help reduce transatlantic flights, while still promoting long distance interactions. The goal of this twinned conference is to bring together experts on Homotopy Theory and adjacent areas to discuss the forefront of current developments in this highly active field.

We especially welcome applications from members of minority groups.

## The tensor HCIZ integral and its relation to enumerative geometry and free probability

## Miniseries on symplectic topology, Talk 2

For zoom details please contact T. Barthel, V. Ozornova, A. Ray, P. Teichner.

## tba

Meeting-ID: 973 8400 7043

For password please contact Stephan Stadler (stadler@mpim-bonn.mpg.de).

## Hall algebras and quantum cluster algebras

The theory of Hall algebras has known many spectacular developments and applications since the discovery by Ringel of their connection with quantum groups. One important object arising naturally in the study of Hall algebras is the integration map defined by Reineke, which allows to produce certain celebrated wall-crossing identities. In this talk I will first focus on the Dynkin case and show how the integration map can be interpreted in a natural way via the representation theory of quantum affine algebras.

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