**Info**

- I am a Ritt Assistant Professor at Columbia University. I graduated from Harvard under the supervision of Professor Benedict Gross in 2015.
- I am interested in number theory.
- Address:
- Math Building 427, MC4430
- Department of Mathematics, Columbia University
- 2990 Broadway
- New York, NY 10027

- Email:

**Research**

*Neron models of Jacobians of Shimura curves of level p^2*, preprint*Remarks on the arithmetic fundamental lemma*(with Yihang Zhu), preprint*Arithmetic intersection on GSpin Rapoport-Zink spaces*(with Yihang Zhu), preprint*Goldfeld's conjecture and congruences between Heegner points*(with Daniel Kriz), preprint*2-Selmer groups, 2-class groups and rational points on elliptic curves*, to appear in*Trans. Amer. Math. Soc.**Level raising mod 2 and obstruction to rank lowering*, to appear in*IMRN*.*Level raising mod 2 and arbitrary 2-Selmer ranks*(With Bao V. Le Hung),*Compos. Math.*152 (2016), no. 8, 1576-1608.

**Teaching**

- I am teaching Math 1101 (Calculus I), Fall 2017.
- 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.

- 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**

- 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