Past Junior Geometry and Topology Seminar

19 June 2014
16:00
Brent Pym
Abstract
Lie algebroids are geometric structures that interpolate between finite-dimensional Lie algebras and tangent bundles of manifolds. They give a useful language for describing geometric situations that have local symmetries. I will give an introduction to the basic theory of Lie algebroids, with examples drawn from foliations, principal bundles, group actions, Poisson brackets, and singular hypersurfaces.
• Junior Geometry and Topology Seminar
12 June 2014
16:00
Omar Kidwai
Abstract
Spectral networks are certain collections of paths on a Riemann surface, introduced by Gaiotto, Moore, and Neitzke to study BPS states in certain N=2 supersymmetric gauge theories. They are interesting geometric objects in their own right, with a number of mathematical applications. In this talk I will give an introduction to what a spectral network is, and describe the "abelianization map" which, given a spectral network, produces nice "spectral coordinates" on the appropriate moduli space of flat connections. I will show that coordinates obtained in this way include a variety of previously known special cases (Fock-Goncharov coordinates and Fenchel-Nielsen coordinates), and mention at least one reason why generalising them in this way is of interest.
• Junior Geometry and Topology Seminar
5 June 2014
16:00
Gerrit Goosen
Abstract
We give an overview of Kitaev's lattice model in the setting of an arbitrary finite group G (where $G = Z_{2}$ is the famous Toric Code). We also exhibit the connection this model has with so-called 123-TQFTs (topological quantum field theories), making use of ideas coming from higher gauge theory and Hopf algebra representations.
• Junior Geometry and Topology Seminar
29 May 2014
16:00
Thomas Wasserman
Abstract
Topological insulators are a type of system in condensed matter physics that exhibit a robustness that physicists like to call topological. In this talk I will give a definition of a subclass of such systems: gapped, free fermions. We will look at how such systems, as shown by Kitaev, can be classified in terms of topological K-groups by using the Clifford module model for K-theory as introduced by Atiyah, Bott and Shapiro. I will be using results from Wednesday's JTGT, where I'll give a quick introduction to topological K-theory.
• Junior Geometry and Topology Seminar
22 May 2014
16:00
TBA
Abstract
• Junior Geometry and Topology Seminar
15 May 2014
16:00
Cancelled
Abstract
• Junior Geometry and Topology Seminar