# Lecture

Lecture or course consisting of one or several talks.

## Lecture course by Don Zagier on "Standard and less standard asymptotic methods"

Posted in
Speaker:
Don Zagier
Date:
Tue, 15/02/2022 - 16:00 - Wed, 23/03/2022 - 15:30

Starting February 15, Don Zagier will give a lecture course entitled "Standard and less standard asymptotic methods". This course will be given in collaboration with the IGAP (Institute of Geometry and Physics, a new joint venture between SISSA and ICTP in Trieste).

The course will be streamed from Trieste twice a week (Tu/Th 4-5:30 for the first four weeks and Mo/We 2-3:30 for the last two weeks).

Abstract:

In every branch of mathematics, one is sometimes confronted with the problem of evaluating an infinite sum numerically and trying to guess its exact value, or of recognizing the precise asymptotic law of  formation of a sequence of numbers ${A_n}$ of which one knows, for  instance, the first couple of hundred values.  The course will tell a number of ways to study both problems, some relatively standard (like the Euler-Maclaurin formula and its variants) and some much  less so, with lots of examples.   Here are three typical examples: 1. The slowly convergent sum  $\sum_{j=0}^\infty (\binom{j+4/3}{j})^{-4/3}$   arose in the work of a colleague.  Evaluate it to 250 decimal digits. 2.  Expand the infinite sum  $\sum_{n=0}^\infty (1-q)(1-q^2)...(1-q^n)$ as  $\sum A_n (1-q)^n$, with first coefficients 1, 1, 2, 5, 15, 53, ... Show numerically that  $A_n$  is asymptotic to  $n! * a * n^b * c$  for some real constants $a$, $b$ and $c$, evaluate all three to high precision, and recognize their exact values. 3.  The infinite series  $H(x) = \sum_{k=1}^\infty sin(x/k)/k$  converges for every complex number $x$.  Compute this series to high accuracy when $x$ is a large real number, so that the series is highly oscillatory.

The courses are scheduled as follows:

1 Tue 15-Feb 16.00 - 17-30
2 Thu 17-Feb 16.00 - 17-30

3 Tue 22-Feb 16.00 - 17-30
4 Thu 24-Feb 16.00 - 17-30

5 Tue 01-Mar 16.00 - 17-30
6 Thu 03-Mar 16.00 - 17-30

7 Tue 08-Mar 16.00 - 17-30
8 Thu 10-Mar 16.00 - 17-30

9 Mon 14-Mar 14.00 - 15.30
10 Wed 16-Mar 14.00 - 15.30

11 Mon 21-Mar 14.00 - 15.30
12 Wed 23-Mar 14.00 - 15.30

These will be hybrid courses. All are very welcome to join either online or in person (if provided with a green pass). Venue: Budinich Lecture Hall (ICTP Leonardo Da Vinci Building), for those wishing to attend in person. Zoom: https://unesco-org.zoom.us/j/91274263707

## Lecture course "Standard and less standard asymptotic methods"

Posted in
Speaker:
Don Zagier
Affiliation:
MPIM, Bonn/ICTP, Trieste
Date:
Tue, 15/02/2022 - 16:00 - 17:30

This course will be given in collaboration with the IGAP (Institute of Geometry and Physics, a
new joint venture between SISSA and ICTP in Trieste). The course will be streamed from Trieste
a week.

You can find the description, exact times and Zoom meeting details on the ICTP webpage:
http://indico.ictp.it/event/9872/

## Lecture series by Prof. Don Zagier

Posted in
Speaker:
Don Zagier
Affiliation:
MPIM, Bonn
Date:
Tue, 03/03/2020 - 16:30 - 18:00
Date:
Tue, 10/03/2020 - 16:30 - 18:00
Date:
Tue, 17/03/2020 - 16:30 - 18:00
Date:
Tue, 24/03/2020 - 16:30 - 18:00
Date:
Tue, 31/03/2020 - 16:30 - 18:00
Date:
Tue, 07/04/2020 - 16:30 - 18:00
Date:
Tue, 14/04/2020 - 16:30 - 18:00
Date:
Tue, 21/04/2020 - 16:30 - 18:00
Date:
Tue, 28/04/2020 - 16:30 - 18:00
Date:
Tue, 05/05/2020 - 16:30 - 18:00
Date:
Tue, 12/05/2020 - 16:30 - 18:00
Location:
MPIM Lecture Hall

Time: Tuesdays, 4.30 - 6 pm
Place: MPIM Lecture Hall, Vivatsgasse 7
First lecture: on March 3, 2020, end ?

## Minicourse on Structure of Modular Categories

Posted in
Speaker:
Alexei Davydov
Affiliation:
Ohio University/MPIM
Date:
Fri, 31/05/2019 - 12:00 - 13:00
Location:
MPIM Seminar Room

Modular fusion categories are mathematical structures appearing in mathematical physics (high energy and now condensed matter physics) and low dimensional topology (3d topological field theories).
The course will give an (elementary and example based) introduction to them and their very rough structure theory, governed by
the so-called Witt group of modular categories.

## Felix Klein Lectures

Posted in
Date:
Thu, 16/05/2019 - 10:15 - 12:15
Location:
MPIM Lecture Hall

## Course by Prof. Don Zagier

Posted in
Speaker:
Don Zagier
Affiliation:
MPIM
Date:
Tue, 02/04/2019 - 16:30 - Tue, 02/07/2019 - 18:00
Location:
MPIM Lecture Hall

The course is meant to provide an informal and elementary introduction to
some of the notions of vertex operator algebras and conformal ﬁeld theory,
to the modularity properties of the corresponding characters, and to the
“modular linear diﬀerential equations” satisﬁed by these modular forms

## IMPRS Minicourse on Translation surfaces of infinite-type

Posted in
Organiser(s):
Vincent Delecroix, Ferrán Valdez
Affiliation:
MPIM
Date:
Mon, 06/05/2019 - 10:00 - 12:00

## Colloquium

Posted in
Date:
Thu, 21/02/2019 - 15:00 - Mon, 30/04/2029 - 16:00
Location:
MPIM Lecture Hall

## Mini-course "The Kontsevich (un)oriented graph complex"

Posted in
Speaker:
Arthemy Kiselev
Affiliation:
University of Groningen
Date:
Fri, 07/12/2018 - 10:00 - 16:30

## Vorlesung "Topology of 4-Manifolds"

Posted in
Date:
Tue, 09/10/2018 - 15:15 - 17:00
Location:
MPIM Lecture Hall

## Web talks in Bonn

Posted in
Organiser(s):
Lukas Brantner
Date:
Thu, 24/05/2018 - 16:15 - Fri, 25/05/2018 - 17:00

## Introduction to Surgery

Posted in
Speaker:
Wolfgang Lück
Affiliation:
Universität Bonn
Date:
Thu, 19/04/2018 - 13:15 - 15:00
Location:
MPIM Lecture Hall

## L^2-Betti numbers, I

Posted in
Speaker:
Wolfgang Lück
Organiser(s):
Wolfgang Lück (Universität Bonn), Peter Teichner (MPIM)
Date:
Tue, 24/04/2018 - 15:15 - 17:00
Location:
MPIM Lecture Hall

## Vorlesung "Invariants of knots and 3-manifolds"

Posted in
Organiser(s):
Wolfgang Lück (Universität Bonn), Peter Teichner (MPIM)
Date:
Thu, 12/04/2018 - 13:00 - 15:00
Date:
Thu, 19/04/2018 - 13:00 - 15:00
Date:
Thu, 26/04/2018 - 13:00 - 15:00
Date:
Thu, 03/05/2018 - 13:00 - 15:00
Date:
Thu, 10/05/2018 - 13:00 - 15:00
Date:
Thu, 17/05/2018 - 13:00 - 15:00
Date:
Thu, 24/05/2018 - 13:00 - 15:00
Date:
Thu, 31/05/2018 - 13:00 - 15:00
Date:
Thu, 07/06/2018 - 13:00 - 15:00
Date:
Thu, 14/06/2018 - 13:00 - 15:00
Date:
Thu, 21/06/2018 - 13:00 - 15:00
Date:
Thu, 28/06/2018 - 13:00 - 15:00
Date:
Thu, 05/07/2018 - 13:00 - 15:00
Date:
Thu, 12/07/2018 - 13:00 - 15:00
Date:
Thu, 19/07/2018 - 13:00 - 15:00
 https://basis.uni-bonn.de/qisserver/rds?state=verpublish&status=init&vmfile=no&publishid=139098&moduleCall=webInfo&publishConfFile=webInfo&publishSubDir=veranstaltungV5D1 - Advanced Topics in Topology - Invariants of knots and 3-manifolds -
 Nr.: 611500505     Vorlesung    SoSe 2018     4.0 SWS
 Studiengang: Master of Science   Mathematics (M. Sc.)

## Mini-course: On the Hasse Principle for Divisibility in commutative algebraic groups

Posted in
Speaker:
Affiliation:
University of Calabria/MPIM
Date:
Fri, 13/04/2018 - 10:15 - Fri, 27/04/2018 - 12:00
Location:
MPIM Lecture Hall

The Hasse Priciple is a fundamental topic in number theory. Anyway a complete proof is very seldom showed in undergraduate and graduate courses in number theory. We will decribe this classical result and prove it. After an overview of some long-established local-global principles, we will focus on the recent local-global question for divisibility in commutative algebraic group. In particular we will explain its relation with the Hasse principle for divisibility of elements of the Tate-Shavarevich group in the Weil-Châtelet group.  This latter problem arose as a generalization of a classical question considered by Cassels. We will describe the results achieved for the two problems during the last fifteen years and some questions that are still open.

## Course on Frobenius Manifolds

Posted in
Date:
Tue, 02/05/2017 - 10:15 - 12:00
Location:
MPIM Seminar Room

## Brauer Groups in Algebraic Topology III

Posted in
Speaker:
Jacob Lurie
Affiliation:
Harvard
Date:
Fri, 23/06/2017 - 09:30 - 10:30
Location:
MPIM Lecture Hall

Let $k$ be a field. The collection of (isomorphism classes of) central division algebras over $k$ can be organized into an abelian group $\mathrm{Br}(k)$, called the Brauer group of $k$. In this series of talks, I'll describe some joint work with Mike Hopkins on a variant of the Brauer group which arises in algebraic topology, controlling the classification of certain cohomology theories known as Morava $K$-theories.

## Brauer Groups in Algebraic Topology II

Posted in
Speaker:
Jacob Lurie
Affiliation:
Harvard
Date:
Thu, 22/06/2017 - 09:30 - 10:30
Location:
MPIM Lecture Hall

Let $k$ be a field. The collection of (isomorphism classes of) central division algebras over $k$ can be organized into an abelian group $\mathrm{Br}(k)$, called the Brauer group of $k$. In this series of talks, I'll describe some joint work with Mike Hopkins on a variant of the Brauer group which arises in algebraic topology, controlling the classification of certain cohomology theories known as Morava $K$-theories.

## Some applications of topology to physics III

Posted in
Speaker:
Dan Freed
Date:
Wed, 21/06/2017 - 09:30 - 10:30
Location:
MPIM Lecture Hall

An axiom system for special quantum field theories was introduced over 25 years ago by Segal and Atiyah.
It has been much elaborated and developed, particularly in the topological case.  In these three lectures I will
discuss aspects of this mathematical theory and applications to problems in physics.

## Some applications of topology to physics II

Posted in
Speaker:
Dan Freed
Date:
Tue, 20/06/2017 - 09:30 - 10:30
Location:
MPIM Lecture Hall

An axiom system for special quantum field theories was introduced over 25 years ago by Segal and Atiyah.
It has been much elaborated and developed, particularly in the topological case.  In these three lectures I will
discuss aspects of this mathematical theory and applications to problems in physics.

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