Past Junior Geometry and Topology Seminar

27 February 2014
16:00
Georgia Christodoulou
Abstract
We will talk about the Beilinson-Bernstein localization theorem, which is a major result in geometric representation theory. We will try to explain the main ideas behind the theorem and this will lead us to some geometric constructions that are used in order to produce representations. Finally we will see how the theorem is demonstrated in the specific case of the Lie algebra sl2
  • Junior Geometry and Topology Seminar
20 February 2014
16:00
Roberto Rubio
Abstract
This talk will give an introduction to generalized complex geometry, where complex and symplectic structures are particular cases of the same structure, namely, a generalized complex structure. We will also talk about a sister theory, generalized complex geometry of type Bn, where generalized complex structures are defined for odd-dimensional manifolds as well as even-dimensional ones.
  • 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

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