Research

13) Constructing abelian varieties from rank 3 Galois representations with real trace field, with Raju Krishnamoorthy

12) Families of subvarieties of manifolds with a canonical form, with Federico Moretti and Giovanni Passeri

11) Frobenius trace fields of cohomologically rigid local systems, with Raju Krishnamoorthy, submitted

10) Finite braid group orbits on SL_2-character varieties, with Aaron Landesman and Daniel Litt, submitted

(Talk and Slides for YMSC colloquium | Daniel’s talk at the Fields Medal Symposium)

9) Geometric local systems on the projective line minus four points, with Daniel Litt, submitted

8) Motivic local systems and Maeda's conjecture, submitted

7) Boundedness of trace fields of rank two local systems, submitted

6) Lifts of supersingular abelian varieties with small Mumford-Tate groups, with Abhishek Oswal. published in IMRN

5) Finiteness of reductions of Hecke orbits, with Mark Kisin, Ananth Shankar, and Padma Srinivasan. Journal of the European Mathematical Society (2023)

4) Attractors are not algebraic, with Arnav Tripathy. Compositio Mathematica. 2024; 160(5): 1073-1100.

3) Calabi-Yau threefolds over finite fields and torsion in cohomologies. Under revision

2) Generalized Bockstein maps and Massey products with Yuan Liu, Romyar Sharifi, Preston Wake, and Jiuya Wang. Forum Math. Sigma (2023)

1) Appendix (joint with Sasha Petrov) to "On p-adic uniformization of abelian varieties with good reduction" by Adrian Iovita, Jackson Morrow, and Alexandru Zaharescu. Compositio Mathematica