Department of Mathematics - UC Santa Barbara

Geometry, Topology, and Physics Seminar, Spring 2017

Part of the NSF/UCSB ‘Research Training Group’ in Topology and Geometry

Organizers: Dave Morrison and Zhenghan Wang.
Meets 4:00 - 5:30 p.m. Fridays in South Hall 6635.

Note: for two weeks in May, we shall resume the 3D Quantum Gravity topic from Winter quarter.

Other Quarters: [ Spring, 2017; Wnter, 2017; Fall, 2016; Spring, 2016; Winter, 2016; Fall, 2015; Spring, 2015; Winter, 2014; Fall, 2013; Fall, 2012; Fall, 2011; Winter, 2011; Spring, 2010; Winter, 2010; Fall, 2009; Spring, 2009; Winter, 2009; Fall, 2008; Spring, 2008; Winter, 2008; Fall, 2007; Spring, 2007; Winter, 2007; Fall, 2006 ]

April 7

No meeting

April 14

Dave Morrison (UCSB)

The symmetries of type IIB string theory

Abstract: It has long been believed that the symmetry group of type IIB string theory is $\mathop{\text{SL}}(2,\mathbb{Z})$. While this is true for the action on the bosonic fields of the theory, we will discuss a $\mathbb{Z}_2$ ambiguity for the action on fermionic fields. Thanks to this ambiguity, a compactification of type IIB string theory requires a $\mathop{\text{Spin}}^c$ structure on spacetime rather than a spin structure, which turns out to be a feature rather than a bug.

We will also take steps towards an $\mathop{\text{SL}}(2,\mathbb{Z})$-equivariant formulation of type IIB string theory, relying on the classical theory of elliptic integrals.

Audio [ mp3, m4a ]; Lecture notes.

April 21

No meeting

April 28

No meeting

May 5

Achilleas Porfyriadis (UCSB)

The black hole in 2+1 dimensions

Abstract: Gravity in 2+1 dimensions does not have any propagating degrees of freedom. However, it does contain black holes, namely the Banados-Teitelboim-Zanelli (BTZ) black holes. The BTZ black holes may be understood as quotients of AdS_3 featuring a causal singularly hidden behind their event horizon. Using the Brown-Henneaux central charge of AdS_3 gravity, the entropy of BTZ black holes may be obtained from an application of the Cardy formula in conformal field theory (CFT). This is the simplest example of the AdS/CFT duality.

Lecture notes.

May 12

Mauricio Romo (IAS)

All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern-Simons Theory

Abstract: I'll review some general aspects of complex Chern-Simons theory on hyperbolic 3-manifolds, focusing on the case of gauge group G=SL(2,C). After a brief introduction to the Volume Conjecture (VC), for knot complements and, a very recent mathematical proposal, for closed hyperbolic 3-manifolds, I'll show how complex Chern-Simons theory is related with them and how this connection leads to a novel generalization of the most recently proposed VC for closed 3-manifolds.

Audio [ mp3, m4a ]; Lecture notes.

No more meetings this quarter.