Chao Li's homepage

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:

Research

• Proof of 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
• Prime twists of elliptic curves (with Daniel Kriz), to appear in Math. Res. Lett.
• Goldfeld's conjecture and congruences between Heegner points (with Daniel Kriz), submitted
• 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 8674 (Arithmetic of L-functions).
• 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.

• 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:
  • Chapter I: Endomorphism rings of elliptic curves
  • Chapter II: Supersingular elliptic curves
  • Chapter III: Complex multiplication and singular moduli

Course Notes

• Geometric aspects of p-adic Hodge theory (ongoing)
• 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