Papers

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

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A simple categorification of the geometric Artin reciprocity with p-torsion coefficients.
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*Extensions by K2 and factorization line bundles* (2019, with James Tao). arXiv:1901.08760.

_{ Factorization line bundles on the Beilinson-Drinfeld affine Grassmannian are classified by certain K-theoretic data. }

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

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The theory of quasi-twistings as a way to formalize the degeneration κ→∞ in the global geometric Langlands program; local versions of the construction are available in §4 of my Paris notes.
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*Maximally Frobenius-destabilized vector bundles over smooth algebraic curves*. arXiv:1408.5117. International Journal of Mathematics **28.02** (2017): 1750003.

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When a vector bundle becomes maximally unstable after Frobenius pullback, we can learn a lot about the stability of the bundle itself, and the result is different depending on whether its rank is larger than, equal to, or lower than the characteristic p.
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*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.

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.

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Notes on Vincent Lafforgue's Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale, section 7.
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*What is the Hecke eigenproblem? * pdf.

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Notes on the problem of finding Hecke eigen-D-modules.
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*The Bondal-Orlov reconstruction theorem. * pdf.

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How to recover a smooth projective variety with ample (or anti-ample) canonical bundle from its derived category of coherent sheaves.
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*Deligne's theorems on degeneration of spectral sequences. * pdf.

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Leray spectral sequence and Hodge-de Rham spectral sequence.
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*Finite and abelian affine group schemes. * pdf.

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Cartier duality, étale group schemes, group schemes of multiplicative type.
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*Tensor product of semistable vector bundles over curves in characteristic zero. * pdf.

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Namely, the tensor product is still semistable. Almost all technical ingredients are explained in detail.
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Other things that you may find funny

My face. Link.

Some of my old piano compositions:

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Sonata (2009). Recording (7'50''). Manuscript.
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Notes in b-minor (2009). Recording (1'25'').
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