Workshop on integrable systems
organized by Koji Hasegawa and Hiraku Nakajima
March 12th 13:30 - 14th 14:30, Kyoto university, 6th Bld., room 609
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13:30-14:30 Vladimir Bazhanov (Australian National University)
``Analytic theory of the eight vertex model"
15:00-16:00 Evgeny Feigin (Lebedev Inst. and Moscow independent univ.)
``Character formulas for Kac-Moody cosets"
16:30-17:30 Edward Frenkel (UC Berkeley)
``Ramifications of the geometric Langlands Program" (1/2)
11:00-12:00 Evgeny Mukhin (Indiana University)
``On the Shapiro conjecture"
13:30-14:30 Edward Frenkel (UC Berkeley)
``Ramifications of the geometric Langlands Program" (2/2)
13:30-14:30 Edward Frenkel (UC Berkeley)
``Instantons beyond topological theory"
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Speaker: Edward Frenkel (UC Berkeley)
Title: Ramifications of the geometric Langlands Program
Abstract. I will give an introduction to the global geometric Langlands
correspondence. In the unramified case it is supposed to attach Hecke
eigensheaves on the moduli stack of G-bundles on a smooth projective
algebraic curve X to G'-bundles with flat connection on X, where G' is the
Langlands dual group of G. But what if we are given a G'-bundle on X with
a flat connection that has singularities, or ramification, at finitely
many points of X? In this case one expects to attach to it a category of
Hecke eigensheaves on a suitable moduli stack of G-bundles on X with
parabolic (or level) structures at the ramification points. I will discuss
an approach to constructing these categories developed recently by
D.Gaitsgory and myself (see math.QA/0611294), which uses representations
of affine Kac-Moody algebras of critical level.
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Speaker: Edward Frenkel (UC Berkeley)
Title: Instantons beyond topological theory
Abstract. Two-dimensional sigma models with Kahler manifold as a target
possess a remarkable limit, in which they become conformally invariant. Up
to now only the topological sector of these models has been analyzed
explicitly. While this leads to many non-trivial results, such as the
Gromov-Witten invariants, this only captures a small part of the theory. I
will talk about the recent work by A.Losev, N.Nekrasov and myself (see
hep-th/0702137), in which we study the structure of these models beyond
the topological sector, as well as similar models in one and four
dimensions: supersymmetric quantum mechanics and Yang-Mills theory,
respectively.
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Speaker: Evgeny Mukhin (Indiana Universty)
Title: On the Shapiro conjecture
Abstract: The B. and M. Shapiro conjecture states that if a Wronskian
determinant of a space of polynomials has real roots then the space of
polynomials has a basis of polynomials with real coefficients. We present
a proof of this conjecture based on properties of the Gaudin model and
discuss the generalizations related to the XXX model.
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長谷川浩司＠東北大学大学院理学研究科数学専攻
Koji Hasegawa at Mathematical Institute, Tohoku University, Sendai JAPAN