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 Wintersemster 2018/ 2019 geht das Kolloquium inzwischen in die dritte Runde. Das Institut für Mathematik freut sich, Ihnen dieses besondere Format anbieten zu können, an dem sich alle vier Schwerpunkte des Instituts beteiligen.

Der letzte Vortrag für das WiSe 2018/2019 findet am 30. Januar 2019 um 16:45 Uhr

in Raum 711/ 7. OG/ Robert-Mayer-Straße 10 statt.

Kaffee und Tee gibt es ab 16:15 Uhr.


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.



Veranstaltungen WiSe 2018/ 2019








24. Oktober 2018

Valentin Blomer (Universität Göttingen)

Eigenfunctions on arithmetic manifolds

It is a classical problem in analysis to study Laplace eigenfunctions on Riemannian manifolds. Number theory enters the scene if the manifold has additional arithmetic structure, such as a family of Hecke operators. In this talk, I will present methods from number theory, Lie groups and automorphic forms to obtain information on the mass distribution of joint eigenfunctions on various arithmetic spaces, and discuss some applications.








12. Dezember 2018

Sandra Di Rocco (KTH Stockholm)

Discriminants: an interplay between algebra, combinatorics and geometry

The term “discriminant” is well known in relation with low degree univariate equations or ordinary differential equations and it has a well defined geometrical meaning naturally connected to the way our vision grasps geometrical shapes. The discriminant of polynomials with specified shape (when it exists) is an (irreducible) polynomial, whose variables are in coefficients of the assigned shape, vanishing when the corresponding polynomial has multiple roots. Finding the discriminant or at least estimating its degree is a classical, well explored problem in mathematics which still faces many challenges.

Besides its importance in computational mathematics, the discriminant locus carries deep and interesting geometrical and combinatorial insights and is one example of fruitful interplay between classical projective algebraic geometry and convex real geometry.

This interplay will be the main theme of the talk. Besides the classical theory of discriminants, natural generalisations associated to systems of polynomial equations will be presented.








19. Dezember 2018

Jon Keating (Universität Bristol)

Characteristic Polynomials of Random Unitary Matrices, Partition Sums, and Painlevé V

The moments of characteristic polynomials play a central role in Random Matrix Theory. They appear in many applications, ranging from quantum mechanics to number theory. The mixed moments of the characteristic polynomials of random unitary matrices, i.e. the joint moments of the polynomials and their derivatives, can be expressed recursively in terms of combinatorial sums involving partitions. However, these combinatorial sums are not easy to compute, and so this does not give an effective method for calculating the mixed moments in general. I shall describe an alternative evaluation of the mixed moments, in terms of solutions of the Painlevé V differential equation, that facilitates their computation and asymptotic analysis.









30. Januar 2019

Silvia Sabatini (Universität Köln)

12, 24 and beyond: a bridge from reflexive polytopes to symplectic geometry

Mathematics finds itself divided and subdivided into hyper-specialized areas of study, each of them with its own internal beauty.  However, what I find most fascinating is when one can build a bridge between two of these seemingly isolated theories. For instance, (symplectic) geometry and combinatorics have a very strong connection, due to the existence of some special manifolds admitting a torus symmetry. The latter is encoded in a map, called moment map, which "transforms" the manifold into a convex polytope. Hence many combinatorial properties of (some special types of) polytopes can be studied using symplectic techniques.
In this talk I will focus on the class of reflexive polytopes, which was introduced by Batyrev in the context of mirror symmetry, and explain how the "12" and "24" phenomenon for reflexive polytopes of dimensions 2 and 3 can be generalized to higher dimensions using symplectic geometry.