Archiv Kolloquium / Former Colloquia
Diagnosis and initialization methods for differential algebraic equations
14.11.2017, 16:00 Uhr
Differential algebraic equations (DAEs) arise in many applications, such as the simulation of constraint multibody systems, electrical networks, the discretization of PDEs, etc. In general, the quality of the numerical solutions of DAEs depends on assumptions that are often not checked rigorously. Consequently, simulations may fail or, even worse, may deliver arbitrary results.
In this talk, we discuss some specific difficulties of DAEs and illustrate them with several examples. Particular emphasis will be placed on the determination of the so-called index of the DAE, the diagnosis of singular points, and the computation of consistent initial values using a projector-based approach. Moreover, we present how automatic differentiation (AD) can be used in this context.
Diana Estévez Schwarz was born in 1972, studied mathematics at the Technische Universität Berlin and received her PhD in 2000 from the Humboldt Universität zu Berlin. Afterwards, she worked as development engineer for circuit simulation software at Infineon Technologies in Munich before she obtained a professorship at the Technische Fachhochschule Berlin in 2006, that was renamed Beuth Hochschule für Technik Berlin in 2009. Her research is focused on differential algebraic equations, in particular, for the computation of the index as well as consistent initial values, the characterization of structural properties and the diagnosis of singularities.
Curvature on graphs
12.07.2017, 14:15 Uhr
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.
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
16.05.2017, 12:15 Uhr
Vortragssaal der Universitätsbibliothek E.21
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.
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.