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Short course on Infinite-dimensional Lie algebras and integrable systems

Short course on Infinite-dimensional Lie algebras and integrable systems
by Takashi Otofuji (Nihon University)

Waseda University
8-29 January 2021
real time Zoom lectures*


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 recognizing 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).


Event details

Venue: Room: real time Zoom lectures*
Languages: English
Lecturer : Takashi Otofuji (Nihon University)
Participants: Open to all students, faculty members, and the general public
Registration: No registration required
Admission: Free

* Registered students will receive Zoom log in information via Waseda Moodle. Visitors/guests are welcome to attend. In order to receive Zoom log in information, please send an e-mail to Martin Guest (martin at stating your name, university affiliation, and position/student status.


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]



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


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