## Upcoming conferences & activities

## Workshop on "$\infty$-categories and their applications", August 17 - 21, 2020

### Update!

The workshop will take place remotely. More information and the program will follow.

## 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.

## Algebraic spaces and Algebraic stacks

In this talk, after recalling the notion of a stack over an arbitrary site, I will introduce the notions of an algebraic space, an algebraic stack and a Deligne-Mumford stack. I will then introduce some examples and properties of these "generalized schemes".

https://bbb.mpim-bonn.mpg.de/b/rei-xh2-kg6

For password email to rkramer@mpim...

## Online: Noncommutative Weil conjectures

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

The Weil conjectures (proved by Deligne in the 70's) played a key role in the development of modern algebraic geometry. In this talk, making use of some recent topological "technology", I will extended the Weil conjectures from the realm of algebraic geometry to the broad noncommutative setting of differential graded categories. Moreover, I will prove the noncommutative Weil conjectures in some interesting cases.

## Online: Buildings, quaternions and Drinfeld-Manin solutions of Yang-Baxter equations

To be useful in theoretical physics, mathematical structure

## Finite descent and the Lawrence--Venkatesh method

If Y is a curve of genus at least 2 over a number field, then the finite descent obstruction cuts out a subset of the adelic points, which is

conjecturally equal to the set of rational points. In particular, we expect this set to be finite. In this talk, I will present ongoing work with Jakob

Stix proving that certain projections of the finite descent locus are finite, as predicted by this conjecture. The method we employ can be

loosely described as "Lawrence--Venkatesh for Grothendieck's section set".

## 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.

## IMPRS Minicourse

## Representation theory learning seminar

## Extra talk

## A study group on Milnor invariants

## IMPRS seminar on various topics: Hitchin systems

## 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.

## Finite descent and the Lawrence--Venkatesh method

If Y is a curve of genus at least 2 over a number field, then the finite descent obstruction cuts out a subset of the adelic points, which is

conjecturally equal to the set of rational points. In particular, we expect this set to be finite. In this talk, I will present ongoing work with Jakob

Stix proving that certain projections of the finite descent locus are finite, as predicted by this conjecture. The method we employ can be

loosely described as "Lawrence--Venkatesh for Grothendieck's section set".

## Online: Buildings, quaternions and Drinfeld-Manin solutions of Yang-Baxter equations

To be useful in theoretical physics, mathematical structure

## Workshop on "$\infty$-categories and their applications", August 17 - 21, 2020

### Update!

The workshop will take place remotely. More information and the program will follow.

## Online: Noncommutative Weil conjectures

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

The Weil conjectures (proved by Deligne in the 70's) played a key role in the development of modern algebraic geometry. In this talk, making use of some recent topological "technology", I will extended the Weil conjectures from the realm of algebraic geometry to the broad noncommutative setting of differential graded categories. Moreover, I will prove the noncommutative Weil conjectures in some interesting cases.

## Algebraic spaces and Algebraic stacks

In this talk, after recalling the notion of a stack over an arbitrary site, I will introduce the notions of an algebraic space, an algebraic stack and a Deligne-Mumford stack. I will then introduce some examples and properties of these "generalized schemes".

https://bbb.mpim-bonn.mpg.de/b/rei-xh2-kg6

For password email to rkramer@mpim...

## Online: Homotopy and Stratification in Arithmetic Geometry

https://bbb.mpim-bonn.mpg.de/b/gae-a7y-hhd

## Definition and examples of stacks

As motivation, we will start by considering the category of continuous functions and illustrate some gluing properties that make it a stack over the category of topological spaces. We will then give the definition of a stack and explore some other examples of stacks coming from algebraic geometry.

https://bbb.mpim-bonn.mpg.de/b/rei-xh2-kg6

For password email to rkramer@mpim...

## Online: L-series values of twists of elliptic curves

We consider certain families of sextic twists of the elliptic curve y^2=x^3+1 that are not defined over Q, but over Q[sqrt(-3)]. We compute a formula that relates the value of the L-function L(E_D, 1) to the square of a trace of a modular function at a CM point. Assuming the Birch and Swinnerton-Dyer conjecture, when the value above is non-zero, we recover the order of the Tate-Shafarevich group and show that its value is a square.

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