[geometry-ml:00755] "A New Recursion from Random Matrices and Topological String Theory": a mini workshop at IPMU

[Satoshi Kondo]

Dear colleagues:

I am pleased to announce the following conference by IPMU.
Please see also our webpage (http://www.ipmu.jp/seminars/).

Regards,

Satoshi Kondo (IPMU)

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IPMU Mini Workshop
A New Recursion from Random Matrices and Topological String Theory

【Date】
December 11(Thu) – 13(Sat), 2008

【Place】
Seminar Room @IPMU Prefab.B, Kashiwa Campus
(Access: http://www.ipmu.jp/access/index.html)

【Organizers】
Akihiro Tsuchiya (IPMU) <akihiro.tsuchiya ＠ ipmu.jp>
Motohico Mulase (Davis)

【Speakers】
Bertrand Eynard (Saclay)
Motohico Mulase (Davis)
Kyoji Saito (IPMU)
Akihiro Tsuchiya (IPMU)

【Schedule】
11 (Thursday)
 9:00 - 10:30 Eynard 1
11:00 - 12:00 Mulase
13:30 - 15:00 Eynard 2

12 (Friday)
 9:00 - 10:30 Eynard 3
11:00 - 12:00 Tsuchiya
14:00 - 15:00 Saito

13 (Saturday)
10:00 - 11:30 Eynard 4

【Titles】
Bertrand Eynard (Saclay)
1. Topological recursion in Random Matrix Theory
2. Topological string theory and the recursion
3. Mathematical implications of the topological recursion
4. Most recent developments

Motohico Mulase (Davis)
Deformation of tau functions and the Eynard-Orantin topological
recursion

Kyoji Saito (IPMU)
Primitive forms of types A_{\frac{1}{2}\infty} and D_{\frac{1}{2}\infty}

Akihiro Tsuchiya (IPMU)
Triplet Vertex Operator Algebras W(p) and Quantum group at
root of unity

 【Synopsis of the Workshop】

 This mini workshop is devoted to the search for a mathematical foundation of a
newly discovered topological recursion by Eynard and Orantin, which was
further generalized by Bouchard, Klemm, Marino and Pasquetti, in the context of
topological string theory. The recursion is originated in Random
Matrix Theory as
an effective tool to calculate free energies and n-point correlation
functions of the
resolvent of Hermitian matrix models. Here the technique involved is a simple
complex analysis on a hyperelliptic curve that appears as the resolvent set of
Hermitian random matrices.

 When applied as an axiom to an arbitrary plane analytic curve, the topological
recursion calculates an infinite sequence of differentials and symplectic
invariants of the curve. A natural question arises: What are these quantities
calculating?

 Miraculously, a particular choice of the curve, the spectral curve of
the theory,
re-constructs the Witten-Kontsevich theory. Moreover, by deforming
this spectral
curve, the recursion reproduces the generalizations of the Witten-Kontsevich
theory due to Mulase-Safnuk and Liu-Xu. Amazingly, a particular specialization
of the deformation also gives the Mirzakhani recursion formula for the
Weil-Petersson volume of the moduli spaces of bordered hyperbolic
surfaces.

 BKMP further show that when the curve is defined by the Lambert W-function,
the recursion provides an effective formula to compute linear Hodge integrals
and Hurwitz numbers. This formula has been unknown to the mathematics
community.

 Even more miraculous is the claim of BKMP that the Eynard-Orantin recursion
computes the Gromov-Witten invariants of toric Calabi-Yau 3-folds through
mirror symmetry. An attempt of understanding the BCOV anomaly equation is
also proposed by Dijkgraaf-Vafa.

 In this mini workshop we provide an ample time to learn the origin of the
topological recursion from its discoverer, Bertrand Eynard. He will
also talk about
the new derivation of Witten-Kontsevich theory and its
various generalizations, as well as his most recent results.

 Mulase will talk about an integrable system approach to the topological
recursion using a deformation theory of tau-functions (joint work with
Safnuk, in
preparation).