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 SoSe 2019 geht das Kolloquium inzwischen in die vierte Runde. Das Institut für Mathematik freut sich, Ihnen dieses besondere Format anbieten zu können, an dem sich alle vier Schwerpunkte des Instituts beteiligen.

Kaffee und Tee gibt es ab 16:15 Uhr.

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 10.07.2019 spricht Frau Noela Müller

zum Thema "Random graphs and phase transitions"

 

 

Veranstaltungen WiSe 2018/ 2019

 

 

 

 

 

 

 

24. April 2019

Karl-Theodor Sturm (Universität Bonn)

Optimal transport, heat flow, and Ricci curvature on metric measure spaces

We present a brief survey on the theory of metric measure spaces with synthetic lower Ricci bounds, initiated by the author and by Lott/Villani, and developed further by Ambrosio/Gigli/Savare and by many others. Particular emphasis will be given to recent breakthroughs concerning the local structure of RCD-spaces by Mondino/Naber and by Brue/Semola and to rigidity results. For instance, given an arbitrary RCD(N-1,N)-space (X,d,m), then

∫  ∫ cos d(x,y) dm(x) dm(y) ≤  0
 
if and only if N is an integer and (X,d,m) is isomorphic to the N-dimensional round sphere. Moreover, we study the heat equation on time-dependent metric measure spaces and its dual as gradient flows for the energy and for the Boltzmann entropy, resp. Monotonicity estimates for transportation distances and for squared gradients will be shown to be equivalent to the so-called dynamical convexity of the Boltzmann entropy on the Wasserstein space which is the defining property of super-Ricci flows. Moreover, we show the equivalence with the monotone coupling property for pairs of backward Brownian motions as well as with log Sobolev, local Poincare and dimension free Harnack inequalities.

  
                           

 

 

 

 

 

 

 

15. Mai 2019

Andrea Colesanti (Universität Florenz)

Valuations on spaces of functions

A valuation is, roughly speaking, a real-valued mapping defined on a family of sets, which is finitely additive. A class of sets for which valuations have been intensively studied is that of convex bodies (compact convex subsets of the n-dimensional Euclidean space). The beauty of the theory of valuations on convex bodies resides, in my opinion, in the elegance and the profundity of some of the results that have been proved within this area. For instance, Hadwiger’s theorem states that intrinsic volumes form a basis of rigid motion and continuous valuations; McMullen homogeneous decomposition theorem and Alesker’s density theorem are of similar fundamental importance.

Recently, the notion of valuation found a natural adaptation in the context of spaces of functions: one just needs to replace, in the finite additivity condition, union and intersection by pointwise maximum and minimum. How much of the theory of valuations on convex bodies can be extended to the functional setting? And how? These questions have not been answered yet, and are the main motivation for my research in this area.

  
                           

 

 

 

 

 

 

 

05. Juni 2019

Michel Brion (Universität Grenoble)

Automorphism groups of compact complex manifolds

The automorphism group of a compact complex manifold is known to be a complex Lie group, and hence an extension of a discrete group (the group of components) by a complex connected Lie group. The talk will discuss the group of components, which is quite mysterious. It is easy to see that this group is generally infinite. Recently, Lesieutre, Dinh and Oguiso constructed examples for which the group of components is not finitely generated, thereby answering a long-standing question by the negative. On the other hand, this group turns out to be finitely presented for some interesting classes of manifolds, starting with complex tori.

    
                           

 

 

 

 

 

 

 

10. Juli 2019

Mihyun Kang (TU Graz)

Topological aspects of random graphs

In this talk we shall discuss various topological aspects of random graphs. How quickly does the genus of a random graph grow as the number of edges increases?  How do topological constraints (such as imposing an upper bound on the genus) influence the structure of a random graph?