In this talk, I will review the notion of modular functor and explain how one use it to defines bundles over the compactified moduli space of Riemann surfaces. The Chern classes of these bundles turn out to define Cohomological field theories. I will explain how this implies that they can be computed by an inductive procedure called topological recursion. One of the motivating example is the study of the so-called Verlinde bundle associated to Wess-Zmino-Witten Conformal field theories.

Based on a joint work with Andersen and Borot

We consider non-interacting particles subject to an external electric potential $V$ and a self-generated magnetic field $B$. The total energy includes the magnetic field energy $\beta \int B^2$ and we minimize over all particle states and magnetic vector potentials (of finite field energy). We estimate the total ground state energy of the system in the semiclassical limit $h \rightarrow 0_{+}$. The relevant parameter measuring the field strength in the semiclassical limit is $\beta h$. We prove that when $\beta h \rightarrow +\infty$ the effect of the self-generated magnetic field is negligible in the sense that we recover the standard, non-magnetic Weyl asymptotics in this case.

This is joint work with L. Erd\”{o}s and J. P. Solovej.

Notes

Le club de maths reprend ses activités après la pause de la semaine dernière. Venez nombreux, venez avec de nouveaux problèmes ou avec des solutions d'anciens problèmes. Toutes les suggestions sont les bienvenues.

François Laudenbach et moi-même vous invitons à un groupe de lecture en topologie: de la "Conjecture de Mumford généralisée" prouvée par Madsen-Weiss, on lira la preuve "for geometrically-minded topologists" publiée par Eliashberg-Galatius-Mishachev

Y. Eliashberg, S. Galatius, N. Mishachev, "Madsen-Weiss for geometrically minded topologists", Geometry & Topology 15 (2011), 411–472;

gt-v15-n1-p13-p.pdf

les mercredis, 14h-16h 1ère séance le 8 mars en salle de séminaires.