Infinite Dimensional Grassmannians
This is an introductory course in algebra and geometry of infinite dimensional Grassmannians. We will start by reviewing the algebraic geometry of finite-dimensional Grassmannians, Plucker embedding and Young tableaux followed by the introduction of Ind-varieties and Co-Ind-varieties. We will then cover algebraic approach to the Sato-Segal-Wilson infinite Grassmannian and study its various applications.
Lecturer
Date
11th September ~ 11th December, 2024
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday,Friday | 10:40 - 12:15 | A14-202 | ZOOM 05 | 293 812 9202 | BIMSA |
Prerequisite
Undergraduate class in Abstract Algebra and some familiarity with elementary Algebraic Geometry are recommended. Otherwise, the course will be as self-contained as possible with necessary topics introduced along the way.
Reference
1. W. Fulton. Young tableaux: with applications to representation theory and geometry. No. 35. Cambridge University Press, 1997.
2. S. Kumar. Kac-Moody groups, their flag varieties and representation theory. Vol. 204. Springer Science & Business Media, 2012.
3. M. Sato. Soliton equations as dynamical systems on infinite dimensional Grassmann manifold. North-Holland Mathematics Studies. Vol. 81. North-Holland, 1983. 259-271.
4. G. Segal, and G. Wilson. Loop groups and equations of KdV type. Publications Mathématiques de l'IHÉS 61 (1985): 5-65.
2. S. Kumar. Kac-Moody groups, their flag varieties and representation theory. Vol. 204. Springer Science & Business Media, 2012.
3. M. Sato. Soliton equations as dynamical systems on infinite dimensional Grassmann manifold. North-Holland Mathematics Studies. Vol. 81. North-Holland, 1983. 259-271.
4. G. Segal, and G. Wilson. Loop groups and equations of KdV type. Publications Mathématiques de l'IHÉS 61 (1985): 5-65.
Audience
Undergraduate
, Advanced Undergraduate
, Graduate
, Postdoc
Video Public
Yes
Notes Public
Yes
Language
English
Lecturer Intro
I studied Applied Mathematics and Physics at the Moscow Institute of Physics and Technology, where I earned both my B.Sc. and M.Sc. degrees. In 2013, I joined the graduate program in Mathematics at Rutgers, The State University of New Jersey, and completed my Ph.D. in 2018 under the guidance of Prof. V. Retakh. After earning my doctorate, I held postdoctoral positions at the University of California Berkeley, the Centre de Recherches Mathématiques in Montreal, and the University of Toronto. In July 2024, I became an Associate Professor at the Beijing Institute of Mathematical Sciences and Applications (BIMSA)