**Info**

- I am an Assistant Professor at Columbia University. I graduated from Harvard under the supervision of Professor Benedict Gross in 2015.
- My research interests: Number Theory, Arithmetic Geometry, Automorphic Forms.
- Address:
- Math Building 614, MC4430
- Department of Mathematics, Columbia University
- 2990 Broadway
- New York, NY 10027

- Email:
- Automorphic Forms and Arithmetic Seminar

**Research**

- Fine Deligne-Lusztig varieties and arithmetic fundamental lemmas (with Xuhua He and Yihang Zhu),
*preprint* - Proof of (Fourier-Jacobi) arithmetic fundamental lemma for the minuscule case (with Yihang Zhu)

An appendix to Yifeng Liu, Fourier-Jacobi cycles and arithmetic relative trace formula,*preprint* - On the 2-part of the BSD conjecture for quadratic twists of elliptic curves (with Li Cai and Shuai Zhai),
*submitted* - Recent developments on quadratic twists of elliptic curves (survey)

*Proceedings of the First Annual Meeting of the ICCM*, to appear - Prime twists of elliptic curves (with Daniel Kriz)

*Math. Res. Lett.*, to appear - Goldfeld's conjecture and congruences between Heegner points (with Daniel Kriz)

*Forum Math. Sigma*, to appear - Arithmetic intersection on GSpin Rapoport-Zink spaces (with Yihang Zhu)

*Compos. Math.*, 154 (2018), No. 7, 1407-1440, doi:10.1112/S0010437X18007108 - Remarks on the arithmetic fundamental lemma (with Yihang Zhu)

*Algebra Number Theory*, 11 (2017), No. 10, 2425-2445, doi:10.2140/ant.2017.11.2425 - 2-Selmer groups, 2-class groups and rational points on elliptic curves

*Trans. Amer. Math. Soc.,*doi:10.1090/tran/7373 - Level raising mod 2 and obstruction to rank lowering

*Int. Math. Res. Not. IMRN*, doi:10.1093/imrn/rnx188 - Level raising mod 2 and arbitrary 2-Selmer ranks (With Bao V. Le Hung)

*Compos. Math.*152 (2016), no. 8, 1576-1608, doi:10.1112/S0010437X16007454

**Teaching**

- I am teaching Math 6657 (Class Field Theory), Spring 2019.
- I taught Math 8674 (Arithmetic of L-functions), Fall 2018.
- I taught Math 1101 (Calculus I), Fall 2017 and Spring 2018.
- I taught Math 6657 (Class Field Theory), Spring 2017.
- I taught Math 1101 (Calculus I) and Math 4043 (Algebraic Number Theory), Fall 2016.
- I taught Math 1101 (Calculus I), Fall 2015 and Spring 2016. (Columbia Departmental Teaching Award)
- I CAed Math 123 (theory of rings and fields) and Math 223b (class field theory 2), Spring 2015. (Harvard Certificate of Distinction in Teaching)
- I taught Math 21a (multivariable calculus), Fall 2013 and Fall 2014. (Harvard Certificate of Distinction in Teaching)
- I CAed Math 223b (class field theory 2), Spring 2013. (Harvard Certificate of Distinction in Teaching)
- I CAed Math 223a (class field theory), Fall 2012. (Harvard Certificate of Distinction in Teaching)
- I taught Knots and Primes, Summer 2012.
- I taught Math 21a (multivariable calculus), Fall 2011.

**Expository Notes**

- By clicking the orange links below, you solemnly swear to send me any mistakes you find.

- Moonshine and the BSD conjecture (a Student Mathematics Colloquium talk)
- Basic functions and the arc space of L-monoids
- Quadratic polynomials and modular forms (a UMS talk)
- Higher Gross-Zagier formulas: Cohomological spectral decomposition and finish the proof
- Kato's explicit reciprocity laws
- The Hodge-Tate period map and the cohomology of Shimura varieties
- Vector bundles on the Fargues-Fontaine curve

- Lusztig's classification of irreducible representations of reductive groups over finite fields
- K2 and L-functions of elliptic curves (a Trivial Notions talk)
- Mixed Tate motives, algebraic K-theory and multiple zeta values
- Applications of Deligne's Weil II
- Kolyvagin's conjecture
- Almost mathematics
- Deligne-Lusztig curves (a Trivial Notions talk)
- What is the Tate conjecture?
- Basic Dieudonne theory
- Eisenstein descent and rational points on modular curves
- Mumford curves (a Trivial Notions talk)
- What is the Birch and Swinnerton-Dyer conjecture?
- Elliptic Surfaces and Mordell-Weil Lattices
- Heights and Finiteness theorems of abelian varieties
- Enriques classification of complex algebraic surfaces
- Stable vector bundles on curves
- Shimura Curves (a Trivial Notions talk)
- Endomorphism rings of elliptic curves and singular moduli — my minor thesis:

**Course Notes**

- Relative trace formulae and the Gan-Gross-Prasad conjectures (ongoing)
- Geometric aspects of p-adic Hodge theory
- Bloch-Kato conjectures for some polarized motives
- Langlands correspondence for general reductive groups over function fields
- Perverse sheaves and fundamental lemmas

- Intersection theory in algebraic geometry
- Galois Representations
- Pure Motives and Rigid Local Systems
- Topics in Automorphic Forms
- Class field theory: proofs
- Class field theory
- Abelian varieties
- Representation theory and number theory
- Perverse sheaves in representation theory
- Discrete subgroups of Lie groups and discrete transformation groups
- Arithmetic surfaces and successive minima
- Teichmuller Theory