Frankfurter Seminar - Kolloquium des Instituts für Mathematik

Die Idee: 4 Schwerpunkte = 1 Kolloquium

Im Wintersemester 2017/18 hat das Institut für Mathematik das "Frankfurter Seminar" ins Leben gerufen. Zum WiSe 2019/ 2020 geht das Kolloquium inzwischen in die fünfte Runde. Das Institut für Mathematik freut sich, Ihnen dieses besondere Format anbieten zu können, an dem sich alle vier Schwerpunkte des Instituts beteiligen.

Das Frankfurter Seminar findet immer mittwochs statt.

An den jeweiligen Veranstaltungstagen wird mit dem Ginkgo-Seminar gestartet. Einer exklusiven Veranstaltung von Doktoranden für Doktoranden, Post-Docs und interessierte Studierende.

Kaffee und Tee gibt es ab 16:15 Uhr.

Um 16:45 Uhr starten die Vorträge unserer Gastwissenschaftler für alle Interessierten.

Ginkgo-Seminar

Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende

Vor jedem Vortrag findet für Doktoranden, Post-Docs und interessierte Studierende ein Vorkolloquium statt, um die Vorträge "aus der anderen Ecke des Instituts" für alle Interessierten zugänglicher zu machen.

Das Vorkolloquium findet immer ab 15.00 (c.t.) in Raum 711 groß vor dem jeweiligen Vortrag statt.

Am 15. Januar 2020 spricht Theresa Kumpitsch

zum Thema "Die Grad-Geschlecht Formel für komplex-projektive Kurven".

Am 29. Januar 2020 spricht Adrien Schertzer

zum Thema "Stochastische Homogenisierung"

 

Veranstaltungen WiSe 2019/ 2020

 

 

 

 

 

 

 

30. Oktober 2019

Sam Payne (UT Austin)

Tropical curves, graph homology, and top weight cohomology of M_g

I will discuss the topology of a space of stable tropical curves of genus g with volume 1. The reduced rational homology of this space is canonically identified with the top weight cohomology of M_g and also with the homology of Kontsevich's graph complex. As one application, we show that H^{4g-6}(M_g) is nonzero for infinitely many g. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of a recent theorem of Willwacher, that homology of the graph complex vanishes in negative degrees, using the identifications above and known vanishing results for M_g. And we prove a formula for the S_n-equivariant Euler characteristic of M_{g,n}, which was conjectured by Zagier.

 

  
                           

 

 

 

 

 

 

 

27. November 2019

Mohab Safey El Din (Sorbonne Université)

On solving polynomial systems over the reals and applications in robotics

Polynomial systems arise in many areas of engineering and computer sciences such as signal theory, cryptography, biology and robotics. In this talk, we will focus on the analysis of kinematic singularities in robotics, which is a fundamental problem in mechanism design. This analysis boils down to a core algorithmic issue in effective real algebraic geometry: given a polynomial system with real coefficients, how to count the number of connected components of their real solution set (or answer connectivity queries on this set)? We will review recent (mathematical and algorithmic) results which yield practically efficient algorithms to solve these problems using computer algebra methods and report on their implementations which can already solve concrete problems in robotics.

  
                           

 

 

 

 

 

 

 

15. Januar 2020

Hansjörg Geiges (Universität zu Köln)

The topology of global surfaces of section

Global surfaces of section were introduced by Poincaré in the context of celestial mechanics, allowing him to reduce the search for periodic orbits in the 3-body problem to finding periodic points of the return map on the surface of section. They continue to play an important role in modern symplectic dynamics. In this talk I shall concentrate on some simple topological aspects of global surfaces of section. In particular, I plan to discuss the topology of surfaces of section for the Hopf flow on the 3-sphere. This leads to an intriguing proof of the degree-genus formula for complex projective curves, using ideas motivated by symplectic dynamics.

This talk is based on joint work with Peter Albers and Kai Zehmisch.

    
                           

 

 

 

 

 

 

 

29. Januar 2020

Felix Otto (MPI Leipzig)

Effective behavior of random media

In engineering applications, heterogeneous media are often described in statistical terms. This partial knowledge is sufficient to determine the effective, i.e. large-scale behavior. This effective behavior may be inferred from the Representative Volume Element (RVE) method. I report on last years' progress on the quantitative understanding of what is called stochastic homogenization of elliptic partial differential equations: optimal error estimates of the RVE method and the homogenization error, and the leading-order characterization of fluctuations. Methods connect to elliptic regularity theory and to concentration of measure arguments.