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## Integrable Systems in Quantum Theory |

Many physical
theories such as quantum field theory and string theory exhibit important connections with integrable systems. We mention two
instances where they are. The first amazing connection is from the the generating function of intersection
numbers of Morita-Mumford classes, matrix models and classical integrable systems of Khadomtsev- Petviashvilii type. For the Korteweg
de Vries equation the first step of this conjecture was proved by Kontsevich and the second by Kharchev,
Marshakov, Mironov, Morozov and Zabrodin. The second striking relation became visible when it was conjectured and
proved that another class of integrable systems, the so-called Toda hierarchies, lay at the foundation
of the Gromov-Witten
invariants of projective space. It forms a key element in Givental's
proof of mirror symmetry for these spaces. Now mirror symmetry is a duality, where two seemingly
different physical theories can be shown to be isomorphic by taking quantum
corrections into account. As such it is a rich
common research area for both mathematicians
and physicists. Integrability can be of great use, e.g., to verify
connections between different theories such as the AdS/CFT-
correspondence that states that a string theory on Anti-de Sitter space
is equivalent to a Conformal Field Theory on its boundary.
At the
conference we will discuss a number of aspects of the rich interaction between integrable
systems and quantum theory. More in particular, we want to focus on the following connections: 1) Progress in the AdS/CFT-
correspondence and integrable systems 2) New developments around the role of integrable systems in Seiberg-Witten
theory 3) Algebraic geometric aspects of the
relevant spaces and [Back] |