Li, Yu 李昱


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..


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.


  1. Y. Li: Wonderful compactification of a Cartan subalgebra of a semisimple Lie algebra. In preparation, to be posted on the arXiv very soon.
  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.


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.


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