(Paul Klee: Senecio, 1922)

About me

I am a 5th year PhD student interested in algebraic geometry and representation theory

My advisor is Dennis Gaitsgory

I have a Curriculum Vitae

Contact

yifei@math.harvard.edu
Science Center 321g
1 Oxford Street
Cambridge, Massachusetts 02138

Papers

7. Tame twistings and Θ-data (2020). arXiv:2004.09671.

6. p-torsion étale sheaves on the Jacobian of a curve (2019). arXiv:1909.12462.

5. Extensions by K2 and factorization line bundles (2019, with James Tao). arXiv:1901.08760.

4. Quantum parameters of the geometric Langlands theory (2017). arXiv:1708.05108.

3. Maximally Frobenius-destabilized vector bundles over smooth algebraic curves. arXiv:1408.5117. International Journal of Mathematics 28.02 (2017): 1750003.

2. Limiting behavior of Donaldson's heat flow on non-Kähler surfaces (2014, with Jacob McNamara). arXiv:1403.8037.

1. Lifting representations of finite reductive groups: a character relation (with Jeffrey Adler et al). arXiv:1205.6448. Involve, a Journal of Mathematics 9.5 (2016): 805-812.

Thesis

Geometric metaplectic parameters. (Last update: April, 2020.) It is a compilation of three papers above (4, 5, 7) on the same theme, with a joint preliminaries section.


Teaching: étale cohomology (Fall 2019)
Here is the course homepage.

Seminar: ind-coherent sheaves (Spring 2016)
Seminar on derived algebraic geometry, with an emphasis on the theory of ind-coherent sheaves. Here is the seminar homepage.


Notes
(Warning: I make mistakes! If you find them, email me.)

Pro-excision of algebraic K-theory. pdf.
Notes on the pro-excision theorem for abstract blow-up squares due to Kerz-Strunk-Tamme.

Cayley-Hamilton theorem and Eichler-Shimura relations. pdf.
Notes on Vincent Lafforgue's Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale, section 7.

What is the Hecke eigenproblem? pdf.
Notes on the problem of finding Hecke eigen-D-modules.

The Bondal-Orlov reconstruction theorem. pdf.
How to recover a smooth projective variety with ample (or anti-ample) canonical bundle from its derived category of coherent sheaves.

Deligne's theorems on degeneration of spectral sequences. pdf.
Leray spectral sequence and Hodge-de Rham spectral sequence.

Finite and abelian affine group schemes. pdf.
Cartier duality, étale group schemes, group schemes of multiplicative type.

Tensor product of semistable vector bundles over curves in characteristic zero. pdf.
Namely, the tensor product is still semistable. Almost all technical ingredients are explained in detail.


Other things that you may find funny

My face. Link.

Some of my old piano compositions:
Sonata (2009). Recording (7'50''). Manuscript.
Notes in b-minor (2009). Recording (1'25'').