Felix Klein Lectures 2022 with Jacob Lurie
Felix Klein Lectures 2022
organised by the HCM. Please find the official website of the event here.
A Riemann-Hilbert Correspondence in p-adic Geometry
Jacob Lurie (Institute for Advanced Studies, Princeton)
Dates:
Lecture 1: MPI, Tuesday, Nov 15, 12:00--13:00;
Lecture 2: MPI, Thursday, Nov 17, 14:00--15:00;
Lecture 3: MPI, Tuesday, Nov 22, 16:30--17:30;
Lecture 4: MPI, Thursday, Nov 24, 14:00--15:00;
Lecture 5: MPI, Tuesday, Nov 29, 16:30--17:30;
Lecture 6: MPI, Thursday, Dec 1, 14:00--15:00.
Venue: MPIM lecture hall
Members of the Bonn mathematics community do not have to apply for participation via this platform. Access to the lecture hall will be granted to them on a first come first served basis until all available seats are taken. The registration for external people is already closed.
Abstract:
At the start of the 20th century, David Hilbert asked which representations can arise by studying the monodromy of Fuchsian equations. This question was the starting point for a beautiful circle of ideas relating the topology of a complex algebraic variety X to the study of algebraic differential equations. A central result is the celebrated Riemann-Hilbert correspondence of Kashiwara and Mebkhout, which supplies a fully faithful embedding from the category of perverse sheaves on $X$ to the category of algebraic $\mathfrak{D}_X$-modules. This embedding is transcendental in nature: that is, it depends essentially on the (archimedean) topology of the field of complex numbers. It is natural to ask if there is some counterpart of the Riemann-Hilbert correspondence over nonarchimedean fields, such as the field $\mathbf{Q}_p$ of $p$-adic rational numbers. In this series of lectures, I will survey some of what is known about this question and describe some recent progress, using tools from the theory of prismatic cohomology (joint work with Bhargav Bhatt).Image source: https://commons.wikimedia.org/wiki/File:Felix_Klein.jpeg
Lectures on minimal 3-manifolds
Lectures on "Topics in 4-manifolds"
Contact: Peter Teichner, Rob Schneiderman
Lecture course by Don Zagier on "Standard and less standard asymptotic methods"
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"
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
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
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
Course by Prof. Don Zagier
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
Colloquium
Mini-course "The Kontsevich (un)oriented graph complex"
Vorlesung "Topology of 4-Manifolds"
Web talks in Bonn
Introduction to Surgery
L^2-Betti numbers, I
Vorlesung "Invariants of knots and 3-manifolds"
https://basis.uni-bonn.de/qisserver/rds?state=verpublish&status=init&vmfile=no&publishid=139098&moduleCall=webInfo&publishConfFile=webInfo&publishSubDir=veranstaltung V5D1 - 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
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
Brauer Groups in Algebraic Topology III
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.
© MPI f. Mathematik, Bonn | Impressum & Datenschutz |