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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: [
Fall, 2021;
Winter, 2020;
Fall, 2019;
Spring, 2018;
Winter, 2018;
Fall, 2017;
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
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| April 14 |
Dave Morrison (UCSB)
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.
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| April 21 |
No meeting
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| April 28 |
No meeting
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| May 5 |
Achilleas Porfyriadis (UCSB)
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.
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| May 12 |
Mauricio Romo (IAS)
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.
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No more meetings this quarter.
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