• The Seiberg-Witten equations and the length spectrum of hyperbolic 3-manifolds, with Francesco Lin.  Submitted.
• How large is A_g(F_q)?, with Jacob Tsimerman. Duke Math Journal (2018).
• Geometry of the smallest 1-form eigenvalue on hyperbolic manifolds, with Mark Stern.  GAFA (2018).
• Cohen Lenstra Heuristics for Étale Group Schemes and Symplectic Pairings, with Jacob Tsimerman.  Compositio Mathematica, accepted for publication. 
• Detecting large simple rational Hecke modules for Γ_0(N) via congruences, with George Schaeffer.  IMRN, accepted for publication.
• On Bhargava's heuristics for GL_2(F_p)-number fields and the number of elliptic curves of bounded conductor. Experimental Mathematics, accepted for publication.
• Twisted limit formula for torsion and cyclic base change, with Nicolas Bergeron. Journal de'l École polytechnique - Mathématiques (2017).
• Equivariant torsion and base change. Algebra and Number Theory (2015).
• The equivariant Cheeger-Muller theorem on locally symmetric spaces. JIMJ (2016).

• Algorithms for the topology of arithmetic groups and Hecke actions, with Aurel Page. Slides 1, Slides 2, Summary.
• On the Cohen-Lenstra heuristics in the presence of roots of unity, with Will Sawin and Jacob Tsimerman.  Summary.
• Polarization counting for abelian varieties over finite fields, with Jacob Tsimerman. Summary.
• Growth of torsion for weight 1 modular forms, with Gerard Freixas i Montplet and George Schaeffer. Summary.

• Taylor-Wiles primes
• p-divisible groups
• Faltings' finiteness theorems
• Baily-Borel compactifications

Teaching

• Math 346/377 (Winter 2019)
• Math 348/398 (Fall 2019)