# Mathematics Colloquium Fall 2018

For further information please call the Mathematics Department at 459-2969

**Tuesday, October 9th, 2018**

**TBA**

**Tuesday, October 16th, 2018**

**David Stork**

**Tuesday, October 23rd, 2018**

**TBA**

**Tuesday, October 30th, 2018**

**Ovidiu Muntean, University of Connecticut**

**TBA**

**Tuesday, November 6th, 2018**

**TBA**

**Tuesday, November 13th, 2018**

**Richard Taylor, Stanford University**

**Tuesday, November 20th, 2018**

**Colin Guillarmou, Paris-Sud**

**Tuesday, November 27th, 2018**

**Pedro Morales, University of California Santa Cruz**

*Spectral Zeta Functions and their applications to the Casimir Effect.*

In this talk, I will explore the Spectral Zeta Function associated with an elliptic (pseudo) differential operator on a compact Riemannian manifold. In this setting, the operator is self-adjoint and unbounded, preventing us for a well define trace and determinant. The Zeta Function formalism enables us to define a zeta-regularized trace for the differential operator, as well as a functional determinant. One direct application of this is in QFT effect, such as the vacuum energy and the Casimir Effect. These have to do with the fluctuations of quantum vacuum producing a non-zero vacuum energy that could produce an attractive or repulsive force depending on the boundary conditions.

**Tuesday, December 4th, 2018**

**TBA**