Infinite dimensional Lie algebras are a key ingredient in the study of those partial differential equations known as integrable systems, just as finite dimensional Lie algebras are used in the case of ordinary differential equations. Various classical phenomena (such as the existence of infinitely many conserved quantities, and the existence of infinite dimensional symmetry groups) can be understood by recognising the relevant Lie algebra and its representations. In these lectures several important examples will be used to illustrate this approach.
Each lecture will include ample time for discussion and questions. Graduate students and researchers in mathematics, physics, and engineering are welcome (see below for registration information).
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Friday January 8, 10:40-12:10
Monday January 11, 10:40-12:10
Friday January 15, 10:40-12:10
Monday January 18, 10:40-12:10
Friday January 22, 10:40-12:10
Monday January 25, 10:40-12:10
Friday January 29, 10:40-12:10 [if possible, face-to-face at Nishi-Waseda Campus] [updated 1/12: Zoom lecture]
1. Lie algebras with triangular decomposition
2. Projective representations
3. The Virasoro algebra
4. Representations of the Virasoro algebras
5. Boson-fermion correspondence
6. The KP hierarchy
7. Other integrable systems
Some references (will be updated):
Kac, Raina, Rozhkovskaya: Bombay lectures on highest weight representations of infinite dimensional Lie algebras. Second edition. World Scientific Publishing, 2013
* Registered students will receive Zoom log in information by e-mail. Visitors/guests are welcome to attend. In order to receive Zoom log in information, please send an e-mail to Martin Guest (martin at waseda.jp) stating your name, university affiliation, and position/student status.
The course is an activity of the
Mathematics and Physics Unit "Multiscale Analysis, Modelling and Simulation" Top Global University Project, Waseda University
Students may register to obtain credit for this course (MATX72ZL Advanced Study of Nonlinear Mechanics).
These lectures are also supported by the Institute for Mathematical Science, Waseda University