Abstracts

A joint Math-Physics workshop:
Strings, Quantum Field Theory and Statistical Mechanics
Supported by the Center for Pure and Applied Mathematics
UC Berkeley
May 9-13, 2005
Organizers: Mina Aganagic, Ori Ganor, Petr Hořava, Nicolai Reshetikhin, and Bruno Zumino.

David Berenstein, Wed 9:30, [Slides (requires QuickTime)]
Aspects of integrability in the AdS/CFT correspondence

Jim Bryan, Mon 2:00
An amazing tetrahedron of dualities

ABSTRACT:
We explain how the following four theories are equivalent:

The equivariant quantum cohomology of Hilb^d(C^2), the Hilbert scheme of degree d points in the plane,
The equivariant orbifold quantum cohomology of Sym^d(C^2), the (orbifold) dth symmetric product of the plane,
The degree d, all genus, equivariant, relative Gromov-Witten theory of P^1xC^2, and
The degree d, equivariant, relative Donaldson-Thomas theory of P^1xC^2.

Giovanni Felder, Thu 2:00
Relative formality theorem and quantization of coisotropic submanifolds

Sergei Gukov, Tue 9:30
The Geometry of Knot Homologies

Anton Kapustin, Fri 9:30
Chiral de Rham complex and the half-twisted sigma-model

Joanna Karczmarek, Thu 9:30
Nonsinglet sectors of Lorentzian c=1 Matrix Model

Mikhail Khovanov, Tue 11:30
Matrix factorizations and link homology

Allen Knudsen, Wed 2:00
Equivaraint cohomology of the Brauer loop stochastic process

Barak Kol, Tue 3:00
String Theory Seminar

Sergei Lukyanov, Thu 11:30, [Slides]
Dual form of the paperclip model

ABSTRACT:

The "paperclip model" is 2D model of Quantum Field Theory with boundary interaction defined through special constraint imposed on the boundary values of massless bosonic fields [hep-th/0312168]. Here we argue that the paperclip model admits equivalent "dual" description, where the boundary constraint replaced by special interaction of the boundary values of the bosonic fields with additional (fermionic) boundary degree of freedom. The dual form involves the topological theta-angle in explicit way.

John McGreevy, Fri 11:30, [Slides]
Topological strings from lattice spins

Andrei Okounkov, Fri 2:00, [Slides]
Quantum cohomology of the Hilbert scheme

Hirosi Ooguri Mon 9:30, [Slides]
Topological string and black holes

Rahul Pandharipande, Mon 11:30
Gromov-Witten/Donaldson-Thomas correspondence

Albert Schwarz, Tue 2:00, [Slides]

Some results and conjectures about topological strings

ABSTRACT:

I would like to talk about some questions related to the paper written together with S. Gukov and C. Vafa and presented at this workshop by S. Gukov. I will discuss also some results obtained together with Yujun Chen and M. Kontsevich in the analysis of Givental's twisted loop group acting on the space of 2D TQFT's and formulate some related conjectures.

Paul Zinn-Justin, Wed 11:30, [Slides]
Combinatorial properties of integrable stochastic processes

ABSTRACT:

We shall explain the remarkable properties of the O(1) Temperley-Lieb loop model and how they led Razumov and Stroganov to formulate a conjecture relating it to Fully Packed Loops and Alternating Sign Matrices. We shall dicuss a recent proof of a corollary of this conjecture obtained by introducing inhomogeneities in the model and relating it to Izergin-Korepin/Okada determinant formulae. In a second part, we shall discuss the similar properties of the O(1) Brauer loop model and how a similar analysis leads us naturally to questions of algebraic geometry; more precisely, we show that it computes the equivariant cohomology classes of components of a newly introduced scheme and discuss mathematical applications.

Last updated on 5/12/2005.