Geometry working seminar

Talk 1. Mateusz Olechnowicz, Pure Mathematics Department, University of Waterloo

“Group schemes II”

How is an affine group a scheme? The goal of this talk is to make less tenuous the claimed equivalence between group schemes and affine groups. To this end, we shall show that the category of affine schemes is equivalent to the opposite of the category of commutative rings. Time permitting, we will introduce the group schemes that are used by Mazur in his proof of the torsion theorem.

Talk 2. Jimmy He, Pure Mathematics Department, University of Waterloo

“Spectral Shape Analysis”

The statistical study of shapes is complicated by the non-Euclidean nature of shape data, making geometry an essential part of the problem. Spectral shape analysis provides a method of analyzing shapes as Riemannian manifolds using the eigenvalues of the Laplace-Beltrami operator. In this talk, we will look at some properties of the Laplace-Beltrami operator and its spectrum which make it useful in statistics. Numerical methods for finding these eigenvalues and an example of their use in medical imaging will also be discussed.