Kommende Vorträge

Seminar webpage: https://guests.mpim-bonn.mpg.de/bianchi/wiqi.html

Though the number $\pi$ is known to be irrational and transcendental, there are still a lot of open (and non-approachable at the moment) questions about its approximations by rational numbers. Where do such difficulties source from? What is exactly proving that a given (nice) number is irrational? How relevant is the structure of such concrete irrationality proofs? In my talk I will try to highlight these points and to explain why the "structure" is most important, in particular, when it comes to connection with more rational areas in mathematics.

This talk will be a partial survey of topics in homological commutative local algebra. In particular, I will discuss results on depth, homological dimensions, and torsion properties of tensor products and powers, as well as characterizations of Gorenstein and regular rings via (co)homology vanishing. I will also mention related conjectures and open problems in this area.

The Milnor torsion is an invariant of unitary flat vector bundles on closed odd-dimensional manifolds. Its analytic counterpart was introduced by Ray and Singer and the equality of these torsions is the celebrated Cheeger-Müller theorem. In this talk, I will discuss how to extend the Milnor torsion to certain equivariant flat superconnections (or representations up to homotopy) for finite group actions and its relation to analytic torsion of the twisted de Rham complex.