Mathematics
Colloquia, Spring 2008
Talks are at 3:30 p.m. in South Hall, Room 6635
Colloquium Chair: Sergei Gukov
A Graduate Colloquium designed exclusively for graduate students
meets on the remaining Thursdays at the same time and place.
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Thursday
April 3, 2008
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Robbert Dijkgraaf
University of Amsterdam
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Thursday
April 10, 2008
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Craig Tracy
UC Davis
Title: The Asymmetric Simple Exclusion Process
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Thursday
April 17, 2008
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graduate student colloquium
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Thursday
April 24, 2008
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Andras Vasy
Stanford University
Title: Asymptotics of solutions of the wave equation on de Sitter and de Sitter-Schwarzschild spaces
Abstract: We analyze the wave equation on manifolds which have an asymptotically de
Sitter-like structure near infinity. These are Lorentzian analogues of
so-called (Riemannian) conformally compact spaces which have been much
studied recently. De Sitter space (which will be described in the talk) is
an example. In particular, we describe the asymptotic behavior of
solutions of the wave equation at the conformal infinity.
In the second part of the talk the extension of these results to de
Sitter-Schwarzschild spaces is discussed. This is joint work with Richard
Melrose and Antonio Sa Barreto.
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Thursday
May 1, 2008
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Kevin Walker
Station Q
Title: Blob homology
Abstract: We define a chain complex B_*(C, M) (the "blob complex")
associated to an n-category C and an n-manifold M. For n=1, B_*(C,
S^1) is quasi-isomorphic to the Hochschild complex of the 1-category
C. So in some sense blob homology is a generalization of Hochschild
homology to (n>1)-categories. The degree zero homology of B_*(C, M)
is isomorphic to the dual of the Hilbert space associated to M by the
TQFT corresponding to C. So in another sense the blob complex is the
derived category version of a TQFT. If time allows, we will
speculate on possible applications of blob homology to tight contact
structures on 3-manfolds (n=3) and extending Khovanov homology to
general 4-manifolds (n=4).
Note: The majority of the talk will assume no prior knowledge of
derived categories or TQFTs.
This is joint work with Scott Morrison.
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Thursday
May 8, 2008
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Sara Billey
Univ. Washington
Title: Smoothness and Rational Smoothness in Affine Grassmannians
Abstract: In this talk we will introduce a topic at
the intersection of topology, algebraic geometry, representation theory
and combinatorics. The motivation for this work comes from the geometry
associated to Kac-Moody groups, the affine Grassmannian, and loop spaces.
However, the techniques required for our main theorems are simply stated
in terms of combinatorial data including partitions, Weyl groups and root
systems. More specifically, we will consider the question: Which affine
Schubert varieties are smooth or rationally smooth in the affine Grassmannian.
We will give a combinatorial characterization of these properties in terms
of "affine partitions". Computer proofs were essential in the exceptional types.
This is joint work with Stephen Mitchell.
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Monday, Tuesday
May 12-13, 2008
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Ron Donagi
UPenn
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Thursday
May 22, 2008
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Claude Lebrun
Stony Brook
Title: On Four-Dimensional 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 n-manifolds admit such metrics. In this talk, I will describe recent progress regarding a the 4-dimensional case. These results specifically concern 4-manifolds which also happen to carry either a complex structure or a symplectic structure.
Note: This talk will be intended to a broad audience. Students are welcome!
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Thursday
May 29, 2008
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graduate student colloquium
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Thursday
June 5, 2008
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Robert Bryant
MSRI
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