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Program

## Lectures:

Topological quantum field theories and some realizations

**Takashi Kimura**

Boston University

**Abstract**
We will explain the notion of a topological quantum field theory,
its relationship to operads, and some generalizations in the presence of a group action.
We describe a families version of these constructions,
so-called cohomological field theories,
involving the moduli space of complex curves possibly with additional data.
We will describe some geometric realizations of these structures
in Chen-Ruan orbifold cohomology and K-theory,
Gromov-Witten theory, and higher spin theory.

Quantum Landau-Ginzburg model and Singularity theory

**Si Li**

Northwestern University

**Abstract**
We will discuss some application of quantum field theory method
to singularity theory in the three lectures.
Lecture one will be an introduction to perturbative quantum field theory.
In lecture two we discuss some basic ideas of gauge theory and its renormalization/quantization.
In lecture three,
we introduce a quantum field theory associated with a holomorphic function.
We apply the quantization method to the simplest example:
A_1-singularity, and discuss its relation with the KdV hierarchy.

BU_Keio.pdf

problem.pdf