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.
At the University of Chicago, I have taught the following courses.
At the University of Hong Kong, I have T.A.'d the following course.
liyu [at] math [dot] uchicago [dot] edu
Office Eckhart - 3