Institutskolloquium WS 2022/23

Das allgemeine Kolloquium des mathematischen Instituts findet während der Vorlesungszeit donnerstags um 17:15 Uhr im Raum 05-426 (hybrid) statt. Ab 16:45 Uhr gibt es im Hilbertraum (05-432)  Kaffee und Kuchen.

(Teilnahme auch online möglich, Zugangsdaten über den Koll.beauftragten.)

Programm Wintersemester 2022/23

03.11. Prof. Dr. Wadim Zudilin (Radboud University Nijmegen)
Irrationality by experiment

Abstract: The majority of real numbers are irrational, however establishing this for very concrete numbers (like the values of Riemann's zeta function and general L-functions at positive integers) remains a difficult task. In my talk I will (try to) give some insights into how Experimental Mathematics assists us in constructing good rational approximations to the quantities represented by period integrals.

10.11. Prof. Dr. Eduard Feireisl (Academy of Sciences, Prague)
The Euler system in fluid mechanics: Good and bad news

Abstract: We discuss some recent results concerning well/ill posedness of the Euler system describing the dynamics of a compressible viscous fluid. In particular, we address the following topics:
1. Density of the "wild'' data.
2. Euler system as an inviscid limit.
3. Measurable semigroup solution.

24.11. Dr. Emre Sertöz (Univ. Hannover)
Separating period integrals of quartic surfaces

Abstract: Periods form a natural number system that extends the algebraic numbers by adding values of integrals coming from geometry and physics. Because there are countably many periods, one would expect it to be possible to compute effectively in this number system. This would require an effective height function and the ability to separate periods of bounded height, neither of which are even remotely possible in general. I will, however, introduce a separation constant to numerically verify identities coming from integrals related to quartic surfaces in 3-space, i.e., related to K3 surfaces. This is joint work with Pierre Lairez.

1.12. Prof. Dr. Hartmut Monien (Univ. Bonn)
Dessins d'enfants and modular curves associated to the sporadic groups Co3 and Janko2 or how to solve a set of 276 polynomial equations of degree 276 in 276 variables explicitly

Abstract: Dessins d'enfants and their realization as Belyi maps of compact Riemann surfaces were originally discovered by Felix Klein. Their importance and relevance was finally understood by Alexander Grothendieck who rediscovered and named them in his "Esquisse d'un programme" in 1984. The most important aspect of dessins is the operation of the absolute Galois group on them. Accordingly, dessins d'enfants provide fascinating insights and fundamental links between different fields of mathematics like inverse Galois theory, Teichmüller spaces, hypermaps, algebraic number theory and mathematical physics. The sporadic groups Janko 2 and Conway 3 are stabilizers of pair of lines in the 24-dimensional Leech lattice. In my talk I will show how to explicitly construct modular curves with automorphism groups J2 and Co3 using methods from applied mathematics.

08.12. Prof. Dr. Thomas Nikolaus (Univ. Münster)
Higher Algebra and algebraic K-theory

Abstract: This talk is about algebraic K-theory groups (defined by Quillen in the early 1970s). We will review the definition and motivation behind those groups and explain some applications.
Then we try to summarize what is known in terms of computations and explain some recent breakthroughs (based on so-called trace methods). One of the central tools used to achieve this progress is `higher categorical algebra' in the sense of Waldhausen, Lurie and others. As a sample application we cover the recent results on the K-theory of Z/p^n obtained in joint work with Antieau and Krause.

15.12. Brittany Shields, PhD (Univ. of Pennsylvania)
Scientific Diplomacy: Cold War Mathematicians and International Relations
Unfortunately, this talk had to be cancelled / der Vortrag musste leider abgesagt werden.

19.01. Dr. Hans Fischer (Kath. Univ. Eichstädt)
Real Analysis Around 1830/40: Propagation and Further Development of Cauchy's Basic Concepts by Peter Gustav Lejeune Dirichlet
Unfortunately, this talk had to be postponed / wegen Erkrankung des Vortragenden muss der Vortrag auf einen späteren Termin verschoben werden.

26.01. Prof. Dr. Catharina Stroppel (Univ. Bonn)
From Platonic solids to Springer theory and beyond
Abstract: In this talk I want to give a small tour starting from Platonic solids and explain how one might naturally construct spaces/manifolds/varieties which arise in representation theory, more precisely Springer theory and sketch why representation theorists care. From that spaces we will construct a Fukaya type category. The talk is for a general audience.

02.02. Prof. Dr. Lutz Weis (Karlsruher Institut für Technologie)
Regularitätsabschätzungen für stochastische, parabolische Evolutionsgleichung

Abstract: Regularitätsabschätzungen sind wesentlich für den Halbgruppenzugang zu stochastischen, parabolischen Evolutionsgleichungen, die durch den Erzeuger einer analytischen Halbgruppe und einem Wiener Maß auf einem Banachraum mit der UMD Eigenschaft beschrieben werden, z.B. um geeignete Fixpunkträume für nichtlineare Gleichungen formulieren zu können.
Dabei wird eine neue stochastische Maximalfunktion eine wichtige Rolle spielen, um Ideen aus der harmonischen Analysis auf die stochastische Situation anpassen zu können.


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