
Geometry, Topology, and Physics Seminar, Spring 2008
Organizers:
Andreas Malmendier
and Dave Morrison.
Meets 4:00  5:30 p.m. Fridays in South Hall 6635.
Various topics relating geometry, topology, and physics.
Other Quarters: [
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
]
Apr. 3/4 
The Geometry, Topology, and Physics Seminar will meet at 3:30pm.
Robert Dijkgraaf (University of Amsterdam)
Quantum Curves and Random Matrices
These talks will be a part of the
UCSB Distinguished Lectures on "Quantum Curves and Random Matrices" given by the
speaker.
Abstract: I will review recent work that relates topological string
theory, random
matrices and integrable hierarchies, and that leads to a natural `quantum'
deformation of conformal field theories on Riemann surfaces where algebraic curves
are replaced by a noncommutative Dmodules.
Thursday: Audio [ mp3,
wma ];
Lecture
Notes.
Friday: Audio [ mp3,
wma ];
Lecture Notes
[version 1,
version 2].

Apr. 11, 18 
No Meetings

Apr. 25 
David Morrison (UCSB)
Abstract: CalabiYau threefolds are compact Riemannian manifolds with
holonomy SU(3), and as such, are always projective algebraic varieties. As
algebraic varieties, there is a natural generalization to singular
CalabiYau threefolds (although the existence of generalized metrics on
these singular spaces is not known). Moreover, in the application of
CalabiYau threefolds to the study of string compactification, singular
CalabiYau threefolds play an important role. We will review what is known
about the `CalabiYau singularities' on such spaces, with an eye on
recent developments and applications.
Audio [ mp3,wma ];
Lecture Notes.

May 2 
Tudor Dimofte (Cal Tech)
Abstract:
I will talk about recent work with S. Gukov and J. Lenells. Based on a
hyperbolic knot invariant of K. Hikami's, we propose a geometric
statesummodel construction for the partition function of SL(2,C)
ChernSimons theory on hyperbolic threemanifolds. Perturbative
coefficients of the partition function can be computed exactly in this
construction, and we (successfully) compare the results to the
ChernSimons partition function obtained via geometric quantization.
Lecture Notes
[version 1,
version 2,
version 3].

May 12/13 
The Geometry, Topology, and Physics Seminar will meet at 3:30pm.
Ron Donagi (University of Pennsylvania)
These talks will be a part of the
UCSB Distinguished Lectures on "The Geometric Langlands Conjecture" given by the
speaker.
Monday: Arithmetic and Geometry, Abelian and Non Abelian
Abstract: We will describe the Langlands program in general as a conjectural non abelian analogue of well known "abelian" results:
class field theory on the arithmetic side, and the AbelJacobi theory of Riemann surfaces and their Jacobians on the geometric side. One
powerful approach to the geometric Langlands conjectures involves abelianization via Hitchin's integrable system and its spectral curves.
Lecture Notes.
Tuesday:Algebra and Analysis, Classical and Quantum
Abstract: Recent input from physics suggests that the geometric Langlands conjecture, as
formulated by Deligne, Laumon, Beilinson and Drinfeld, can be viewed as a statement in quantum field
theory. This has a classical limit which has now been proved, at least generically. The relationship
between the classical and quantum versions is deep and mysterious. The quantum version can of course
be studied as a deformation of the classical one. But there is tantalizing evidence  from quantum
field theory as well as non abelian Hodge theory  that the full quantum version can also be understood
as a twistor rotation of the classical version.
Audio [ mp3,
wma ];
Transparencies.

May 22 
Claude Lebrun (Stoney Brook)
On FourDimensional Einstein Manifolds
Abstract: An Einstein metric is by definition a Riemannian metric of constant Ricci curvature. One would like to
completely determine which smooth compact nmanifolds admit such metrics. In this talk, I will describe recent progress
regarding a the 4dimensional case. These results specifically concern 4manifolds which also happen to carry either a
complex structure or a symplectic structure.

Jun 5/6 
Robert Bryant (MSRI)
Geometric Flows
This talk will be a part of the
UCSB Distinguished Lectures on "Geometric Flows and Special Holonomy" given by the
speaker.
Thursday: Geometric Flows and Special Holonomy
Abstract:
Geometric flows have been considered by several researchers as an approach to constructing solutions of the special holonomy equations. In this talk, I will examine the nature of these `flows', in particular, their wellposedness and stability. The first nontrivial case, namely SU(2) holonomy in dimension 4, already displays many of the interesting features that are encountered in the exceptional cases (G2 holonomy in dimension 7 and Spin(7) holonomy in dimension 8). The study of these features raises some interesting problems in differential geometry even in dimension 3, as will be explained in the lecture.
Audio [ mp3,
wma ];
Lecture
Notes.
Friday: The Geometry of Riemannian Submersions
Abstract:
A considerable amount of work has been done to classify Riemannian submersions and foliations from space forms, and most of the recent work has concentrated on using nonnegativity of the curvature to prove global rigidity results. Meanwhile, the local nature of the PDE that define Riemannian submersions has received considerably less attention and, in fact, little appears to be known about the local generality of solutions of the underlying overdetermined PDE. In this talk, I will discuss the nature of this overdetermined PDE system, the cases in which the full local solution space is understood and the prospects for understanding the general case. If there is time, I will also discuss what this information could tell us about the global problem of classifying the Riemannian submersions from space forms.
Audio [ mp3,
wma ];
Lecture notes.

Jul 18 
Gregory Moore (Rutgers University)
Abstract:
We give an overview of a project with Dan Freed and Jacques
Distler whose goal is a precise
and general formulation of orientifold backgrounds of type II string theory.
A central theme is the use of twisted
equivariant differential generalized cohomology theories. The Bfield twists
a version of
equivariant KR theory, while the RR fields and currents are formulated in
terms of a twisted
equivariant differential KR theory. One important new result is a formula
for the RR charge of an orientifold
plane at the Ktheory level, which lifts the standard result of
MoralesScruccaSerone in
integral cohomology.
Audio [ mp3,
wma ];
Lecture notes.


