Li, Yu 李昱


About

Hello! I am a Ph.D. student in the Department of mathematics at the University of Chicago, working with Victor Ginzburg.

I received my B.Sc. in mathematics from the University of Hong Kong in 2014.

Here is my C.V..

Research

My research interest lies in the interaction between geometric representation theory and symplectic/Poisson geometry. The problems that I think about usually have to do with deformation quantization, cluster algebras, spherical varieties, (additive) toric varieties, gauge theory, mirror symmetry, etc.
In particular, I am interested in anything that is even remotely related to the standard Poisson bracket on a semisimple Lie group. Examples of such objects include Lie bialgebra, Manin triple, variety of Lagrangian subalgebras, Fomin-Zelevinsky minor, universal centralizer, quantum cohomology, Yang-Baxter equation, quantized universal enveloping algebra, crystal base, quantum boson algebra, abelian ideal, Kazhdan-Lusztig theory for an affine Weyl group, etc.

Up to now, the theory of abelian ideals of a fixed Borel subalgebra of a simple Lie algebra has been dominantly combinatorial. Currently, I am developing a Poisson geometric approach to this theory. I am also trying to develop a theory of additive toric varieties. A prototypical example of such a variety is the wonderful compactification of a Cartan subalgebra of a semisimple Lie algebra.

My research statement is available upon request.

Papers

  1. Y. Li: Wonderful compactification of a Cartan subalgebra of a semisimple Lie algebra. In preparation, to be posted on the arXiv in November.
  2. S. Evens and Y. Li: Abelian ideals and the variety of Lagrangian subalgebras. Submitted. arXiv: 2010.04358.
  3. Y. Li: Quantum boson algebra and Poisson geometry of the flag variety. Submitted. arXiv: 1904.10141.
  4. Y. Li: Gaiotto's Lagrangian subvarieties via loop groups. Submitted. arXiv: 1705.01639.

Teaching

At the University of Chicago, I have taught the following courses.

In addition, I have also T.A.'d the following courses.

At the University of Hong Kong, I have T.A.'d the following course.

Contact

Email liyu [at] math [dot] uchicago [dot] edu
Office Eckhart - 3