Classical groups seen from infinity

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Program

Thursday August 13		Friday August 14
10.45–11.00	Opening remarks
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

Talks

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

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.

Maxim NAZAROV: Yangians and classical Lie algebras

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.

Yuri NERETIN: Double coset multiplication on infinite-dimensional classical groups

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.

Andrei OKOUNKOV: Applied noncommutative geometry
Stanislav SMIRNOV: Conformal invariance and universality in the 2D Ising model

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.

Anatoly VERSHIK: What does it mean “Asymptotic representation theory”?

Venue

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).

Supporting organizations


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.”

Registration form

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