Past Junior Geometry and Topology Seminar

10 March 2016
16:00
Jack Kelly
Abstract

In this talk I will give several perspectives on the role of
quasi-abelian categories in analytic geometry. In particular, I will 
explain why a certain completion of the category of Banach spaces is a
convenient setting for studying sheaves of topological vector spaces on
complex manifolds. Time permitting, I will also argue why this category
may be a good candidate for a functor of points approach to (derived)
analytic geometry.

  • Junior Geometry and Topology Seminar
18 February 2016
16:00
Thomas Wasserman
Abstract

Topological Quantum Field Theories are functors from a category of bordisms of manifolds to (usually) some categorification of the notion of vector spaces. In this talk we will first discuss why mathematicians are interested in these in general and an overview of the relevant notions. After this we will have a closer look at the example of functors from the bordism category of 1-, 2- and 3-dimensional manifolds equipped with principal G-bundles, for G a finite group, to nice categorifications of vector spaces.

  • Junior Geometry and Topology Seminar
4 February 2016
16:00
Lucas Branco
Abstract

Higgs bundles have a rich structure and play a role in many different areas including gauge theory, hyperkähler geometry, surface group representations, integrable systems, nonabelian Hodge theory, mirror symmetry and Langlands duality. In this introductory talk I will explain some basic notions of G-Higgs – including the Hitchin fibration and spectral data - and illustrate how this relates to mirror symmetry.

  • Junior Geometry and Topology Seminar
3 December 2015
16:00
Renee Hoekzema
Abstract

In 1954 Thom showed that there is an isomorphism between the cobordism groups of manifolds and the homotopy groups of the Thom spectrum. I will define what these words mean and present the explicit, geometric construction of the isomorphism.

  • Junior Geometry and Topology Seminar

Pages