Past Junior Geometry and Topology Seminar

6 February 2014
16:00
Lam Yan
Abstract
Quivers are directed graphs which can be thought of as "space" in noncommutative geometry. In this talk, we will try to establish a link between noncommutative geometry and its commutative counterpart. We will show how one can construct (differential graded) quivers which are "equivalent" (in the sense of derived category of representations) to vector bundles on smooth varieties.
  • Junior Geometry and Topology Seminar
30 January 2014
16:00
Alejandro Betancourt
Abstract
Ricci solitons were introduced by Richard Hamilton in the 80's and they are a generalization of the better know Einstein metrics. During this talk we will define the notion of Ricci soliton and I will try to convince you that these metrics arise "naturally" in a number of different settings. I will also present various examples and talk a bit about some symmetry properties that Ricci solitons have. Note: This talk is meant to be introductory and no prior knowledge about Einstein metrics will be assumed (or necessary).
  • Junior Geometry and Topology Seminar
9 December 2013
16:00
Sebastian Novak
Abstract
TQFTs have received widespread attention in recent years. In mathematics for example due to Lurie's proof of the cobordism hypothesis. In physics they are used as toy models to understand structure, especially boundaries and defects. I will present a lattice construction of 2d Spin TFT. This mostly motivated as both a toy model and stepping stone for a mathematical construction of rational conformal field theories with fermions. I will first describe a combinatorial model for spin surfaces that consists of a triangulation and a finte set of extra data. This model is then used to construct TFT correlators as morphisms in a symmetric monoidal category, given a Frobenius algebra as input. The result is shown to be independent of the triangulation used, and one obtains thus a 2dTFT. All results and constructions can be generalised to framed surfaces in a relatively straightforward way.
  • Junior Geometry and Topology Seminar
5 December 2013
16:00
to
17:30
Montse Casals
Abstract
In this talk, we will review the classical Bass-Serre theory of groups acting on trees and introduce its real version, Rips' theory. If time permits, I will briefly discuss some higher dimensional spaces that are currently being investigated, namely cubings and real cubings.
  • Junior Geometry and Topology Seminar
14 November 2013
16:00
to
17:30
Jens-Jakob Kratmann Nissen
Abstract
By using the Weil-Gel'fand-Zak transform of Faddeev's quantum dilogarithm, Andersen and Kasheav have proposed a new state-integral model for the Andersen--Kashaev TQFT, where the circle valued state variables live on the edges of oriented levelled shaped triangulations. I will look at a couple of examples which give an idea of how the theories are coupled.
  • Junior Geometry and Topology Seminar
7 November 2013
16:00
to
17:30
Jan Vonk
Abstract
In this talk, I will describe how the eigenvalues of the Atkin operator on overconvergent modular forms might be related to the classical study of the Laplacian on certain manifolds. The goal is to phrase everything geometrically, so as to maximally engage the audience in discussion on possible approaches to study the spectral flow of this operator.
  • Junior Geometry and Topology Seminar
31 October 2013
16:00
to
17:30
Emily Cliff
Abstract
Motivated by the study of PDEs, we introduce the notion of a D-module on a variety X and give the basics of three perspectives on the theory: modules over the sheaf of differential operators on X; quasi-coherent modules with flat connection; and crystals on X. This talk will assume basic knowledge of algebraic geometry (such as rudimentary sheaf theory).
  • Junior Geometry and Topology Seminar

Pages