(Paul Klee: Senecio, 1922)

About me

I'm a PhD student interested in categorical questions in algebraic geometry

My advisor is Dennis Gaitsgory. When I was an undergraduate, I learned a lot from Aise Johan de Jong

I have a Curriculum Vitae


Science Center 321g
1 Oxford Street
Cambridge, Massachusetts 02138

... Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play. — Alexander Grothendieck « Récoltes et Semailles »


Quantum parameters of the geometric Langlands theory (2017). arXiv:1708.05108.
The theory of quasi-twistings, and the construction of a family of quasi-twistings for the geometric Langlands program.

Maximally Frobenius-destabilized vector bundles over smooth algebraic curves. arXiv:1408.5117. International Journal of Mathematics 28.02 (2017): 1750003.
Essentially, when a vector bundle becomes very, very unstable after Frobenius pullback, we can learn a lot about the stability of the bundle itself (depending on whether its rank is larger than, equal to, or lower than the characteristic p).

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

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.

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 page.

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

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 interesting

The Stacks Project. Link.

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