Koriyama Geometry and Physics Days 2016 "Painleve equations, integrable systems and moduli spaces":
First Series: Geometry and integrable systems around the fusion algebra
Japanese
Feb 6- 8, 2016
5F, Building 55, College of Engineering, Nihon University (Koriyama, Fukushima),
Access to the campus,
Time table from Koriyama station to/from the campus
some hotels near Koriyama Station
We have two aims:
1. to study moduli of vector bundles on Riemann surfaces, focusing on
Witten's paper:
The Verlinde Algebra And The Cohomology Of The Grassmannian;
2. to study integrability in conformal field theory
(Painleve equations, etc)
Second Series of KGPD 2016 is being planned later in 2016.
Time table:
6th
1400-1440 Kaneko: Construction of representations of compact Lie groups and their loop groups
1450-1530 Ueoka: Construction of representations of Lie algebras
1530-1550 Coffee break
1550-1640 Nagoya: On Virasoro conformal blocks 1
1650-1740 Nagoya: On Virasoro conformal blocks 2
7th
1000-1050 Yanagida: Rational CFT and Verlinde algebra 1
1100-1150 Yanagida: Rational CFT and Verlinde algebra 2
1200-1250 (lunch meeting) Otofuji: Quantum cohomology of Grassmannians
1310-1400 Sasano: Spaces of initial conditions of the Painleve systems
1410-1510 Kori: WZW models (Section 2 of Witten's paper and sone generalizations)
Notes
1510-1540 Coffee break
1540-1640 Sako: Topological Field Theories and Gauged WZW model 1
8th
1000-1050 Sako: Topological Field Theories and Gauged WZW model 2
1100-1150 Nakatsu: Quasi-Hamiltonian spaces
1200-1250 (lunch meeting) Guest: From Painleve equations to CFT
1300-1350 Fuji: The Drinfeld-Sokolov hierarchy and equations of Painleve type
1400-1450 Yumibayashi: String/Soliton duality and Triangulated Category of KP Difference Geometry
1500-1600 Discussion with coffee/tea
Speakers and titles (tentative):
Yusuke Sasano (Nihon University/Shibaura Institute of Technology/Chiba Institute of Technology):
Spaces of initial conditions of the Painleve systems
We will discuss the spaces of initial conditions of the Painleve systems from the viewpoint of the following:
(1) Polynomial Hamiltonian systems
(2) Compactification
(3) Accessible singularities
(4) Painleve ƒ¿-method
(5) Resolution of accessible singularities
(6) Holomorphy and symmetry
Kenta Fuji (Kobe):
The Drinfeld-Sokolov hierarchy and equations of Painleve type
The Drinfeld-Sokolov hierarchy is a generalization of the KdV hierarchy and the KP hierarchy obtained by using affine Lie algebras. In this talk we explain the Drinfeld-Sokolov hierarchy so that you should be able follow the calculations .
Next we derive equations of Painleve type by similarity reduction of the Drinfeld-Sokolov hierarchy. Using the equations of Painleve type thus obtained we study the structure of the Drinfeld-Sokolov hierarchy.
Yoshiki Kaneko (Waseda):
Construction of representations of compact Lie groups and their loop groups
I will review the construction of irreducible representations of compact Lie groups and their loop groups, by the Borel-Weil theorem.
Shunsuke Ueoka (Waseda):
Construction of representations of Lie algebras
First, I will review the construction of representations of finite
dimensional complex semisimple Lie algebras using Verma modules.
Second, I will define Kac-Moody algebras. If there is sufficient time,
I will explain some representations of Kac-moody algebras.
Hajime Nagoya (Kanazawa):
On Virasoro conformal blocks
I will explain conformal blocks as expectation values of vertex operators on Virasoro Verma modules, for regular and irregular cases. Topics are the definitions of vertex operators and conformal blocks, free field realization, integral formulas for conformal blocks, Belavin-Polykov-Zamolodchikov equations, connection problems of regular conformal blocks.
Shintarou Yanagida (RIMS):
Rational CFT and Verlinde algebra
I will explain the Verlinde algebra for a rational CFT, focusing on the case of affine vertex algebras (WZW model).
The contents are:
affine Lie algebras, their integrable representations, vertex operator algebras, affine vertex algebras, rationality and $C_2$ cofiniteness, conformal blocks and the Verlinde algebra.
Toshio Nakatsu (Setsunan):
Quasi-Hamiltonian spaces (after Alexeev-Malkin-Meinrenken)
Tosiaki Kori (Waseda):
WZW models (Section 2 of Witten's paper and sone generalizations)
Notes
Akifumi Sako (Tokyo University of Science):
Topological Field Theories and Gauged WZW model
Witten discussed that WZW model as topological field theories in Section 2.5 and Chapter 4 in "The Verlinde Algebra And The Cohomology Of The Grassmannian", Cambridge 1993, Geometry, topology, and physics 357-422 hep-th/9312104.
In this talk, the topological field theories are introduced pedagogically, and some background of the Section 2.5 and a part of Chapter 4 of the Witten's paper is reviewed.
Tsukasa Yumibayashi (TMU):
String/Soliton duality and Triangulated Category of KP Difference Geometry
First, we introduce the (closed) string/soliton duality which is given as duality between tachyon correlation function and tau function. A key point of the duality is the Schottky problem. Next, we give the "KP" difference geometry which is 4 dimensional lattice space for definition of discrete KP equation, and structure of triangulated category of "KP" difference geometry.
Martin Guest (Waseda):
From Painleve equations to CFT
Recent work by Lisovvy et al has uncovered a representation-theoretic structure in the asymptotic data of solutions to Painleve equations. We shall give a (somewhat disjointed) general introduction to this area, from the point of view of Lie groups.
Takashi Otofuji (Nihon University):
Quantum cohomology of Grassmannians
We introduce small quantum cohomology for general Kaehler manifolds and
then give a presentation of the quantum cohomology ring of Grassmannians.
This conference is supported by JSPS Grant-in-Aid for Scientific Research (A) 25247005 (PI:
Martin Guest)
Previous KGPDs:
February 2012
February 2014
October 2014
TMUGS