Kai Xu

kaixu [at] math [dot] harvard [dot] edu

I am a fifth-year mathematics graduate student at Harvard University, interested in algebraic geometry and representation theory related to quantum field theory and string theory. My advisor is S.-T. Yau. I will be graduating in 2023.

Research

All of my preprints can be found on arxiv, also see my google scholar page.

Algebraic Geometry:

• Semiorthogonal decomposition of D^b(Bun_2^L) (joint with S.-T. Yau)

• The orbifold Hochschild product for Fermat hypersurface (joint with S. Huang)

• Affine Schur-Weyl duality and moduli theory (in progress)

Deformation Quantization and Index Theory:

• Geometry of Localized Effective Theories, Exact Semi-classical Approximation and the Algebraic Index (Joint with Z. Gui and S. Li) Commun. Math. Phys. 382, 441–483 (2021)

Quantum Field Theory and String Theory:

• Holography and the KKLT Scenario (joint with S. Lüst, C. Vafa and M. Wiesner) J. High Energ. Phys. 2022, 188 (2022).

• On Upper Bounds in Dimension Gaps of CFT's (joint with T. C. Collins, D. Jafferis, C. Vafa and S.-T. Yau)

Teaching

Math 22A Vector Calculus and Linear Algebra, Fall 2022, Harvard

Math 22B Vector Calculus and Linear Algebra, Spring 2022, Harvard

Tutorial Introduction to Modular Forms, Summer 2020, Harvard

Math 22B Vector Calculus and Linear Algebra, Spring 2020, Harvard