March 9 | Elena Poletaeva
(IAS, Princeton) | Superconformal algebras and semi-infinite
cohomology |
| | Superextensions of the Virasoro algebra are called superconformal algebras. They play an
important role in physics. The well-known examples are the Neveu-Schwarz and Ramond
superalgebras, the $N=2$ and $N=4$ superconformal algebras.
Semi-infinite cohomology, introduced by B. Feigen, is a generalization of the classical Lie
algebra cohomology to the infinite-dimensional case. We show that certain superconformal
algebras act on semi-infinite Weil complexes and cohomology. We also observe an analogy
between relative semi-infinite cohomology and de Rham cohomology in K\"ahler geometry.
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April 4 | Yong-Geun Oh
(U. of Wisconsin) | Seidel's long exact sequence of symplectic Floer
cohomology on Calabi-Yau manifolds |
| | In this lecture, we will explain how the Dehn twist along a Lagrangian sphere on a
Calabi-Yau manifold induces a long exact sequence of Floer cohomology on the set
of certain distinguished collection of Lagrangian submanifolds, which we call Calabi-
Yau Lagrangian branes. This is the analog to the long exact sequence that Seidel
introduced in the context of exact Lagrangian branes.
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April 27 | Zhang-Ju Liu
(Peking Univ.) | Omni-Lie algebroids |
| | We define a notion called Omni-Lie algebroid generalizing the omni-Lie algebras
introduced by A. Weinstein. We prove that Lie algebroid structure on a vector bundle
E are one-to-one correspondent to the Dirac structures coming from a bundle map
from the jet bundle of E to the gauge Lie algebroid of E. This work is joint with Z. Chen.
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May 2 | Jinho Baik
(Courant Institute) | Asymptotics of Tracy-Widom distribution functions in
random matrix theory, and total integral of Painleve
solutions |
| | The Tracy-Widom distribution functions are certain probability distribution functions
expressed in terms of Fredholm determinants or in terms of a solution of the Painleve II
equation. These distribution functions arise in random matrix theory, statistics, combin-
atorics and probability. The asymptotic expansion of these functions at negative infinity
has been known except for the constant term. We discuss the question of evaluating the
constant term, which will be expressed in terms of the Barnes G-function, and also
discuss the total integral of the Painleve II solution.
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