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Thursday August 13 |
Friday August 14 |
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10.45–11.00 | Opening remarks |
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11.00–12.15 | A. Kirillov | 11.00–12.15 | I. Krichever |

12.15–12.45 | Coffee break |
12.15–12.45 | Coffee break |

12.45–14.00 | A. Vershik | 12.45–14.00 | A. Okounkov |

14.00–15.30 | Lunch |
14.00–15.30 | Lunch |

15.30–16.45 | Yu. Neretin | 15.30–16.45 | S. Smirnov |

16.45–17.15 | Coffee break |
16.45–17.15 | Coffee break |

17.15–18.30 | M. Nazarov | 17.15–18.30 | A. Borodin |

19.00 | Conference dinner |

**Alexei BORODIN**: Interlacing particle systems**Alexandre KIRILLOV**: Family algebras and generalized exponents**Igor KRICHEVER**: Integrable systems and geometry of moduli spaces of curves with punctures**Maxim NAZAROV**: Yangians and classical Lie algebras**Yuri NERETIN**: Double coset multiplication on infinite-dimensional classical groups**Andrei OKOUNKOV**: Applied noncommutative geometry**Stanislav SMIRNOV**: Conformal invariance and universality in the 2D Ising model**Anatoly VERSHIK**: What does it mean “Asymptotic representation theory”?

The celebrated Novikov's conjecture: the Jacobians of curves are exactly those indecomposable principally polarized abelian varieties (ppav) whose theta-functions provide explicit solutions of the Kadomtsev–Petviashvili (KP) equation, was the first evidence of the now well-accepted usefulness of combining the techniques of integrable systems and algebraic geometry to obtain new results in both fields.

In the talk we will discuss certain structures and constructions of the Whitham theory, an essential part of the perturbation theory of soliton equations, and show that they can be instrumental in understanding the geometry of the moduli spaces of Riemann surfaces with marked points.

One of the discoveries of G. I. Olshanski is the link between the classical Lie algebras and affine quantum groups, namely Yangians. I my talk, I will review the link. I will also review the most recent progress in the area, including explicit realizations of irreducible representations of Yangians, and remarkable appearance of Yangians in the theory of finite W-algebras.

We consider discuss this double coset multiplication (discovered by Olshanski), identify these cosets with space of intereior matrix valued functions (in the spirit of V. Potapov) or with a certain space of rational curves in Grassmannian.

2D Ising model at criticality is considered a classical example of conformal invariance in statistical mechanics, which is used in deriving many of its properties. However, no mathematical proof has ever been given, and even physics arguments support (a priori weaker) Möbius invariance.

We will discuss how discrete holomorphic observables appear in the Ising model and lead to a rigorous proof of conformal invariance and universality. This allows not only to prove predictions originating in physics, but also improve many of them.

Based on a joint work with D. Chelkak and C. Hongler.

The meeting will take place in Moscow, on August 13–14, 2009, at the premises of the A. A. Kharkevich Institute for Information Transmission Problems. See access map here.

Your local contacts are Dr Andrei Sobolevski (ansobol@mccme.ru, Skype name andrei.sobolevskii) and Ms Liza Kryukova (secretary@poncelet.ru).

A. A. Kharkevich Institute for Information Transmission Problems | The Russian Foundation for Basic Research | EADS Foundation | Laboratoire J.-V. Poncelet |

This meeting benefited from the support of “EADS Foundation Chair in mathematics.”

Last modified: Tue Aug 11 00:18:27 MSD 2009