Infinite Analysis

Infinite Analysis

Infinite Analysis 09
~ New Trends in Quantum Integrable Systems ~

We plan to hold an international workshop on quantum integrable systems in July, 2009. The purpose is to bring together active researchers from around the world and to discuss most recent progress in integrable systems and related mathematical areas. This workshop is in spirit a continuation of those at RIMS, Kyoto University, started in 1991. The most recent was a series of workshops held in 2004 as the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems". It is already 4 years since, and many exciting developments have emerged during the time. We hope that our workshop will fill this gap, encourage international cooperation, and, more importantly, stimulate young researchers in related fields. The subjects to be discussed include:
  • Correlation functions of solvable models
  • Integrable models in quantum field theory
  • Conformal field theory
  • Mathematical aspects of Bethe ansatz
  • Special functions and integrable differential/difference equations
  • Representation theory of infinite dimensional algebras
  • Integrable models and combinatorics 
Organizing Committee:
Boris Feigin (Landau), Michio Jimbo (Rikkyo), Tetsuji Miwa (Kyoto), Masato Okado (Osaka), Takeshi Suzuki (Okayama), Kouichi Takemura (Yokohama City Univ.), Yoshihiro Takeyama (Tsukuba), Yuji Yamada (Rikkyo)
Infinite Analysis 11
~ Frontier of Integrability ~

We plan to hold an international workshop on integrable systems in July 2011. This is the third session in a series of "Infinite Analysis" started in 2009. The purpose in this year is to advance the frontiers of integrability. The workshop focuses on developments in integrable systems and also related disciplines. We hope that our workshop will stimulate researchers in both mathematics and theoretical physics, and encourage international cooperation.

Organizing Committee:
 A. Kuniba (Tokyo), M. Okado (Osaka), Y. Saito (Tokyo), H. Sakai (Tokyo),  J. Shiraishi (Tokyo), Y. Takeyama (Tsukuba), Y. Yamada (Rikkyo)
Infinite Analysis 11 Winter School
Quantum Cluster Algebras and Related Topics

This workshop focuses on "quantum cluster algebra". This is a fast developing subject and this workshop could be the first meeting concentrating on this subject. The workshop has a 3-day school followed by a one-day mini-workshop. For the school we invite four lecturers who play an active role in this subject recently. We ask them 3 lectures on the topics below starting from very elementary part, so a newcomer to this subject can also understand. 

Organizing Committee:
A. Kuniba (Tokyo), T. Nakanishi (Nagoya), M. Okado (Osaka), Y. Takeyama (Tsukuba)

This workshop is supported by Grants-in-Aid for Scientific Research No. 23340007 from JSPS.
Infinite Analysis 13
Infinite Analysis: Past, Present and Future
Bethe Ansatz, Quantum Groups and Beyond

Organizing Committee: 
Atsuo Kuniba (Tokyo), Hiraku Nakajima (RIMS), Tomoki Nakanishi (Nagoya), 
Masato Okado (Osaka), Takahiro Shiota (Kyoto), Yoshihiro Takeyama (Tsukuba)
Infinite Analysis 13 Spring School at Nagoya 
Yangians and quantum loop algebras 

Lecturer: Valerio Toledano Laredo (Northeastern University) 
Date:March 12 (tue) - 14 (thu), 2013 
Place:Graduate School of Mathematics, Nagoya University, Sci Build. 1 Room 109 

March 12 (tue) 10:00-11:30. 13:30-15:00 
March 13 (wed) 10:00-11:30. 13:30-15:00 
March 14 (thu) 10:00-11:30 

Abstract: These lectures are based on joint work with Sachin Gautam. 

They will concentrate on two closely related infinite dimensional quantum groups associated to a complex, semisimple Lie algebra g: the Yangian Y_h(g), and the quantum loop algebra U_q(Lg). The former is a deformation of the current algebra g[s], and the latter of the loop algebra g[z,z^{-1}]. 

It was pointed out by Drinfeld in the 80s that the quantum loop algebra degenerates to the Yangian. In the first part of the lectures, I will show that these two objects are in fact isomorphic after completion, by an appropriate quantum lift of the change of variable z=e^s. 

In the second part, I will review the classification of finite-dimensional irreducible representations of Y_h(g) and U_q(Lg). Assuming that q is not a root of unity, I will then construct an equivalence of categories between finite-dimensional representations of U_q(Lg) and an appropriate subcategory of finite-dimensional representations of Y_h(g). Unlike the isomorphism alluded to above, this equivalence is transcendental, and governed by the monodromy of an additive, abelian difference equation. 
Infinite Analysis 13 Autumn School
Quantum Dilogarithm, Modular Double, and Representation Theory

Organizing Committee: A. Kuniba (Tokyo), T. Nakanishi (Nagoya), M. Okado (Osaka City), Y. Takeyama (Tsukuba)
This workshop is supported by Grants-in-Aid for Scientific Research No. 23340007 from JSPS.
The 14th International Conference, 
Graduate School of Mathematics, Nagoya University

Summer School on Cluster Algebras in Mathematical Physics

Rei Inoue (Chiba), Atsuo Kuniba (Tokyo), Tomoki Nakanishi (Nagoya)
Masato Okado (Osaka City), Yoshihiro Takeyama (Tsukuba)

Advisory Committee
Philippe Di Francesco (Illinois at Urbana-Champaign)