Perspectives in Mathematical Science I
(2021 Spring, Part 1 -- Hamanaka)
News
[Archive]
Syllabus of My Part
- Title of Part 1: Five Lectures on Determinants
- Instructor: Masashi Hamanaka
- Date: Tuesday, 14:45--16:15 (during April 12 -- May 21)
- Room: School of Science Building 1 (Mathematics), Room 509
- Language: English
- Course contents:
Determinants play essential roles in broad areas of mathematics and physics. I would like to discuss various aspects of determinants with relation to algebraic and differential equations. First I will lecture on the basics of determinant theory and introduce various identities, such as the (generalized) Laplace expansion formula, Plucker relation, and so on. Next, I will apply them to problems to solve algebraic equations and differential equations. Finally I would discuss noncommutative versions of determinants, especially quasideterminants, with application to noncommutative integrable equations.
- References (5/10):
- [H] Ryogo Hirota,
The Direct Method in Soliton Theory
(Cambridge UP)
- [MJD] T. Miwa M. Jimbo E. Date,
Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras
(Cambridge UP)
- [T] Teiji Takagi, ``Lecture on Algebra,'' (Iwanami) (in Japanese)
- [S] Mikio Sato (note by Toru Umeda),
``Lectures by Sato Mikio,'' (RIMS lecture note) (in Japanese)
- [M] Motohiko Mulase,
``Algebraic Aspects of Solitons,''
in Bessatsu Suurikagaku ``Solitons'' (1985-10) 127-143 (in Japanese)
- [D] L. Dickey,
``Soliton Equations and Hamiltonian Systems,''
(World Scientific)
- [GGRW] I. Gelfand, S. Gelfand, V. Retakh, R. Wilson,
Quasideterminants, arXiv:math/0208146
- [GKLLRT] I. Gelfand, D. Krob, A. Lascoux, B. Leclerc,
V. Retakh, J.-Y. Thibon,
Noncommutative symmetric functions, arXiv:hep-th/9407124
- Grading: Quiz and Report (Details will be
announced on April 13.)
Resources of handwritten notes and report problem (Updated 5/18)
Tentative Plan and Materials (Updated 5/18)