Research

15) Local systems which do not come from abelian varieties, with Paul Brommer-Wierig, submitted

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

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

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

11) 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)

10) Geometric local systems on the projective line minus four points, with Daniel Litt, accepted to Compositio Mathematica

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

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

7) Lifts of supersingular abelian varieties with small Mumford-Tate groups, with Abhishek Oswal. published in IMRN, Volume 2024, Issue 10, May 2024, Pages 8384–8401

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

5) The Attractor conjecture for Calabi-Yau variations of Hodge structures

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, Volume 11, 2023, e5

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, 158(7), 1449-1476