OIST Mini Symposium: Moduli Space, Conformal Field Theory and Matrix Models

Summary

This mini symposium is for recent new developments of moduli space and conformal field theory. Although this topic was intensively studied around 1990 from mathematics and physics both side, by Witten and Kontsevich, (both Fields medalists) for equivalence with KdV hierarchy, the conjecture of Witten, and Gromov-Witten invariants are still mysterious. 

In this mini symposium, mathematician and physist are expected to discuss together this important developments, and find new directional ways. The conformal field theory (CFT), specially supersymmetric CFT may be an strong approach from physics side, and conformal block seems essential part for understanding KdV and KP, and Gromov-Witten symplectic manifold invariants. Recently, three dimensional Ising model is found to be solvable, by CFT, but usual CFT extension from two dimensions to three dimensions need a lot of studies, and need a new idea.

This year, the first female mathematician, Maryam Mirzakhani (Stanford University) was awarded the 2014 Fields medal, which the most prestigious honor in mathematics. Mirzakhani is the first woman to win the prize, widely regarded as the "Nobel Prize of mathematics," since it was established in 1936. Mirzakhani's recent research further investigates the symmetry of surface geometry, particularly within theories regarding Teichmüller dynamics. In general, her work can best be described as pure mathematics – research that investigates entirely abstract concepts of nature that might not have an immediately obvious application. (Source: Stanford University News, http://news.stanford.edu/news/2014/august/fields-medal-mirzakhani-081214.html, as of Aug.2014). 

Her subject is Moduli space from geometrical side (Teichmuller dynamics), and she could solve the Witten conjecture, which relates the intersection numbers of the curves on Riemann surface to a dynamical soliton equation, KdV hierarchy. This is most important reason for the award of Fields medal.

This mini symposium aims further extension of Mirzakhani work to more complicated geometrical moduli space, for instance non-orientable surface, and to find a new proof for the generalized Witten conjecture, by algebraic method, topological method and field theoretical method, from different approaches. Therefore, this mini symposium is timely organized and it will be attract wide interests from mathematics and physics side.

Speakers

Tohru Eguchi, Rikkyo University, Japan
Hiroshi Itoyama, Osaka City University, Japan
Alexander Alexandrov, ITEP Moscow, Russia
Hao Xu, Pittsburg University, USA
Kunio Obitsu, Kagoshima University, Japan
Ran J. Tessler, Institute of Mathematics, Hebrew University
Takayuki Oda,  Department of Mathematics, University of Tokyo, Japan
Nariya Kawazumi, University of Tokyo, Japan
Shunsuke Tsuji, University of Tokyo, Japan
Takuya Sakasai, University of Tokyo, Japan
Yuuki Tadokoro, Kisarazu National College of Technology
(This list is subject to change. Thank you in advance for your understanding.)

Program & Abstarts

Please see here for the latest program and abstracts (PDF). (as of 2015/3/15)
(This list is subject to change. Thank you in advance for your understanding.)