## 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.

## 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.

## Operads of musical phrases and generation

https://hu-berlin.zoom.us/j/61339297016

## Elliptic curves and chromatic homotopy theory

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For passcode of this talk please contact Tobias Barthel (tbarthel@mpim-bonn.mpg.de)

## New bounds on growth in SL_n

Zoom ID: 992 4902 2878

https://zoom.us/j/99249022878

## tba

## Symmetries of 4-manifolds

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For passcode of this talk please contact Pieter Moree (moree@mpim-bonn.mpg.de)

## tba

## Braid varieties and algebraic weaves

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

## A sparse equidistribution problem for expanding horocycles on the modular surface

The orbits of the horocycle flow on hyperbolic surfaces are classified: each orbit is either dense or a closed horocycle around a cusp. Expanding closed horocycles are themselves asymptotically dense, and in fact become equidistributed on the surface. The precise rate of equidistribution is of interest; on the modular surface, Zagier observed that a particular rate is equivalent to the Riemann hypothesis being true. I will discuss the asymptotic behavior of evenly spaced points along an expanding closed horocycle. This is based on joint work with Uri Shapira and Shucheng Yu.

## 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.

## A study group on Milnor invariants

## IMPRS Minicourse

## IMPRS seminar on various topics: Hitchin systems

## Extra talk

## Representation theory learning seminar

## 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.

## 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.

## A sparse equidistribution problem for expanding horocycles on the modular surface

The orbits of the horocycle flow on hyperbolic surfaces are classified: each orbit is either dense or a closed horocycle around a cusp. Expanding closed horocycles are themselves asymptotically dense, and in fact become equidistributed on the surface. The precise rate of equidistribution is of interest; on the modular surface, Zagier observed that a particular rate is equivalent to the Riemann hypothesis being true. I will discuss the asymptotic behavior of evenly spaced points along an expanding closed horocycle. This is based on joint work with Uri Shapira and Shucheng Yu.

## Braid varieties and algebraic weaves

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For password please contact Christian Kaiser (kaiser@mpim-bonn.mpg.de).

## tba

## Symmetries of 4-manifolds

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For passcode of this talk please contact Pieter Moree (moree@mpim-bonn.mpg.de)

## tba

## New bounds on growth in SL_n

Zoom ID: 992 4902 2878

https://zoom.us/j/99249022878

## Elliptic curves and chromatic homotopy theory

https://zoom.us/j/93172910947

Meeting ID: 931 7291 0947

For passcode of this talk please contact Tobias Barthel (tbarthel@mpim-bonn.mpg.de)

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