# Alexander Petrov

**Category: **Research Fellows

**Affiliation: ** Harvard University

Alexander Petrov will obtain his PhD in 2022 from Harvard University, where he has been advised by Mark Kisin.

Petrov has demonstrated exceptional creativity in proving surprising theorems concerning Galois representations and arithmetic local systems on algebraic varieties. Settling a conjecture of Litt, he proved that geometrically irreducible, arithmetic local systems on varieties over p-adic fields are essentially de Rham. He discovered a deep generalization of Belyi’s famous theorem, showing that any irreducible Galois representation which arises in the cohomology of an algebraic variety over a number field, appears in the space of algebraic functions on the fundamental group of the thrice punctured sphere. And he opened a new range of possibilities with counterexamples to a conjecture of Scholze on Hodge symmetry for rigid analytic varieties.

Alexander was appointed as a Clay Research Fellow for a term of five years beginning 1 July 2022.