Vorträge in der Woche 16.04.2018 bis 22.04.2018

Dienstag, 17.04.2018: On the Deligne-Riemann-Roch isomorphism and the Cappell-Miller torsion

Gerard Freixas i Montplet (Jussieu, Paris)

The Deligne-Riemann-Roch isomorphism lifts the Grothendieck-Riemann-Roch theorem for a vector bundle on a families of curves, to the level of line bundles. When the family of curves is endowed with a Kähler structure, and the vector bundle is endowed with a hermitian metric, the isomorphism becomes an isometry for suitable metrics, involving in particular the Quillen metric. The Quillen metric, in its turn, is defined through Hodge theory and the Ray-Singer holomorphic torsion. A natural question, that arises when studying moduli spaces of flat vector bundles on a Riemann surface, is what happens when, instead of metrics, we have connections. In our context, a candidate to replace the Quillen metric is the torsion invariant introduced by Cappell-Miller. I will explain how their torsion element fits into the picture of the Deligne-Riemann-Roch isomorphism. I will focus on line bundles, and depending on time I will mention what can be done in arbitrary rank. The contents of the talk are based on joint work with Richard Wentworth.

Dienstag, 17.04.2018: Darstellungstheorie von Banach C(K)-Moduln

Henrik Kreidler

"Mit dem Satz von Gelfand ist die Darstellungstheorie kommutativer C*-Algebren gut verstanden. Bereits in den 70er und 80er Jahren wurde auch die Darstellung von Banach-Moduln über solchen C*-Algebren systematisch untersucht. In diesem Vortrag besprechen wir dynamische Versionen der zentralen Ergebnisse dieser Theorie und veranschaulichen diese anhand von Beispielen."

Donnerstag, 19.04.2018: Self-gravitating fluids near the big bang singularity

Dr. Florian Beyer (University of Otago, New Zealand)

In this talk I present results (joint work with P.G. LeFloch) about the construction and analysis of singular self-gravitating fluid models close to the cosmological big bang singularity. In particular I will explain the notion of a "singular initial value problem" and its relationship with the so-called "asymptotically velocity term dominance" and "matter does not matter" conjectures in general relativity.

Donnerstag, 19.04.2018: An adaptive viscosity E-scheme for balance laws

Prof. Dr. Achim Schroll (Universität Odense)

Donnerstag, 19.04.2018: Statistical Mechanics of Repeated Quantum Measurements

Prof. Vojkan Jaksic (McGill University, Montreal, Canada)

The statistics of the (finite alphabet) outcomes of repeated quantum measurements is studied by methods of thermodynamic formalism. Viewed as one-dimensional spin systems with long range interactions, repeated quantum measurements exhibit very rich (and sometimes very singular) thermodynamic behaviour. We will describe general thermodynamical formalism of these systems and illustrate its unexpected features on a number of examples. This talk is based on joint works with T. Benoist, N. Cuneo, Y. Pautrat, and C-A. Pillet.