MRIT
6th Workshop
Math-for-Industry Tutorial：
Spectral theories of non-Hermitian operators
and their application
- Sponsor:
Mathematical Research Center for Industrial Technology (MRIT)
Kyushu University - Date:
March 19(Thu) - 20(Fri), 2009 - Place:
The major conference room of Faculty of Science,
Building No.1 of Faculty of Science
(MAP)
Hakozaki Campus, Kyushu University,
6-10-1 Hakozaki, Higashi-ku,
Fukuoka 812-8581, Japan
Lecturers:
- Setsuro Fujiie (University of Hyogo, Japan) [Mathematics]
- Makoto Hirota (Japan Atomic Energy Agency) [Plasma physics]
- Toshiaki Hishida (Nagoya University, Japan) [Mathematics]
- Stefan Llewellyn Smith (University of California, San Diego, USA)
- Sherwin A. Maslowe (MCGill University, Canada)
- Hideo Nakazawa (Chiba Institute of Technology, Japan) [Mathematics]
- Francis Nier (Université de Rennes, France)
- Boris S. Pavlov (University of Auckland, New Zealand)
Organizers:
- Yasuhide Fukumoto (Kyushu University) - chair
- Yoshikazu Giga (University of Tokyo)
- Yoshiyuki Kagei (Kyushu University)
- Yasunori Maekawa (Kyushu University) -secretary
- Kaori Nagatou (Kyushu University)
- Zensho Yoshida (University of Tokyo)
Purpose:
- The traditional approach of using modal expansions is far from sufficient to analyze stability of fluid flows and flowing plasmas. As exemplified by time algebraic growth of disturbances, non-orthogonality of eigen-functions and continuous spectra associated with critical layers etc. offers a rich variety of complicated phenomena in space and time. Novel phenomena, possibly of common mathematical origin, have been found in a diversity of fields including statistical mechanics and cosmology. To grasp some unified picture behind these phenomena, we focus on spectra of non-Hermitian operators. Existence of negative-energy waves and the Casimir invariants reflects non-Hermitian property of the operator describing evolution of fields. As opposed to a Hermitian operator for which the spectral decomposition theory is matured, there is no systematic treatment of using modal decomposition by complete sets of eigen-functions, including singular eigen-functions, as for a non-Hermitian operator, and, moreover, the counterpart of the Jordan normal form is not known for infinite dimensional cases. The concepts of energy and conservation laws take a different guise, and mathematical machinery for them is wanted. In this workshop, specialists will give a series of lectures on basic mathematical notions, current status and novel techniques to handle non-Hermitian operators, whereby we seek a key to tackle with outstanding mathematical problems in industrial technologies.
Contact
- Yasuhide Fukumoto: yasuhide
math.kyushu-u.ac.jp - Yasunori Maekawa: yasunorimath.kyushu-u.ac.jp
- MRIT administrator
Junko Tsukada: tsukadamath.kyushu-u.ac.jp
Tel:092-642-3883, Fax:092-642-2779
Download:
WS06-poster.pdf