Overview
My major mathematical research interests are derived algebraic geometry, algebraic geometry, homological algebra, and homotopy theory. I am also interested in the fields related to derived algebraic geometry such as representation theory, category theory, algebraic topology, complex geometry, and mathematical physics.
Most of my current projects are related to representation homology, which is a DAG object modelling derived representation scheme. I focus on computational aspects of the object and manage to connect the higher information to the original algebro-geometric spaces. I’m very interested in the connections of representation homology with other (co)homology theories.
Research Focus
Derived algebraic geometry, especially the computations, and its links and applications to other areas of mathematics.
Publications
- Guanyu Li. Commuting varieties of upper triangular matrices and representation homology, 2024. arXiv:2403.13953.
- Guanyu Li. A step towards computational derived algebraic geometry: The RepHomology package for macaulay2, 2024. arXiv:2410.18383.