Archiv Kolloquium des Instituts für Mathematik und Informatik


Curvature on graphs

Prof. Dr. Matthias Keller (Universität Potsdam)

12.07.2017, 14:15 Uhr

Seminarraum 1

Franz-Mehring-Str. 47

Abstract

The geometry of a graph is tightly linked the spectral theory of graph Laplacian. In this talk we discuss a notion of curvature on planar graphs which goes back to ideas of Descartes. This notion of curvature is then used to deduce spectral bounds from curvature bounds.

About Prof. Dr. Matthias Keller

Matthias Keller was born in 1980. He studied Mathematics in Chemnitz.

He received his PhD in 2010 from the University of Jena. In 2015 he finished his habilitation also in Jena. He had postdoc and visiting professorship positions in Jerusalem and Haifa before he obtained full professorship in Potsdam. Since 2017 he is a principal investigator in the DFG priority programme "Geometry at Infinity".

The main focus of Matthias Kellers research is on spectral theory of graphs and its relation to spectral geometry of Riemannian manifolds.


Reachability in Generalizations of Topological Spaces - Applications to Evolution and Chemistry

Prof. Dr. Peter F. Stadler

16.05.2017, 12:15 Uhr

Vortragssaal der Universitätsbibliothek E.21

Felix-Hausdorff-Str. 10

Abstract

Reachability is a notion that can, in relatively simple cases, be modeled by non-idempotent closure functions. This picture is sufficient e.g. in the context of biological evolution and evolutionary search. The study of chemical universes, comprising a not necessarily finite set of chemical compound organized by chemical reaction that convert them into each other, however, indicates that generalized closures do not convey all the necessary details: after all, chemical universes are directed hypergraphs. An alternative inroad is to start from the complementary notions of separation and connectedness and to generalize these to a non-symmetric setting. In this presentation I will focus on basic properties of the resulting abstract reachability spaces and on open questions.

About Peter F. Stadler

Peter F. Stadler, born in 1965, received his Ph.D. in Chemistry from the University of Vienna in 1990 following studies in chemistry, mathematics, physics and astronomy. After a PostDoc at the Max Planck Institute for Biophysical Chemistry in Goettingen, he returned to Vienna and qualified as a professor in 1994 in Theoretical Chemistry. Since 1994 he is External Professor at the Santa Fe Institute, a research center focused on Complex Systems. In 2002 he moved to the University of Leipzig as Full Professor of Bioinformatics. Since 2009 he is External Scientific Member of the Max Planck Society and head of the "Discrete Biomathematics" group at the MPI for Mathematics in the Sciences. He is corresponding member abroad of the Austrian Academy of Sciences since 2010.

The general theme of his research is the search for a consistent understanding of biological processes (with an emphasis on (molecular) evolution) at the genotypic, phenotypic, and dynamical level.