Upcoming Talks

Felix Klein Lecture jointly with the MPI-Oberseminar.

Further information: https://math-events.uni-bonn.de/event/260/

Let M be a 3-dimensional compact manifold with non-empty boundary. There exists a collection of tetrahedra stuck in pairs along their faces such that deleting all their vertices gives a space that is homeomorphic to the interior of M. This is called a (ideal) triangulation of M. Amendola, Matveev and Piergallini have shown that any two such triangulations of M are connected by a sequence of triangulations, where each triangulation in the sequence is obtained from the previous one by a local combinatorial change, namely a 2-3 or 3-2 move.

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.