Alexander Petrov

Alexander Petrov is a Clay Research Fellow at the Massachusetts Institute of Technology (MIT), conducting research at the intersection of algebraic geometry, number theory, and homological algebra. He completed his PhD in Mathematics at Harvard University in 2022 under the supervision of Professor Mark Kisin.

Education

• PhD in Mathematics, Harvard University, 2022 (Advisor: Mark Kisin)

Research Interests

Petrov's work centers on advanced problems in arithmetic geometry, particularly in positive characteristic settings. His research investigates structural properties of de Rham complexes, p-adic Hodge theory, and the arithmetic of algebraic varieties, with significant contributions to understanding Galois representations, Brauer groups, and cyclic homology through homological algebra techniques. His methodologies often bridge abstract algebraic frameworks with concrete geometric applications.

Publications Overview

His publication record (2017-2025) reveals a consistent focus on foundational questions in arithmetic geometry, featuring deep explorations of cohomology theories, spectral sequences for algebraic groups, and p-adic local systems. Key trends include the decomposition of de Rham complexes in positive characteristic, violations of Hodge symmetry in rigid-analytic contexts, and universal properties of Galois actions. Collaborations with leading mathematicians like Alexei Skorobogatov and Vadim Vologodsky underscore his integration into the global mathematics community.

Awards and Honors

• Clay Research Fellow (current)

Advising and Collaborations

As a postdoctoral fellow, Petrov was previously advised by Mark Kisin during his doctoral studies at Harvard. No current advisees are mentioned, but his extensive co-authorship network—including frequent work with Skorobogatov and Vologodsky—demonstrates active collaborative research. His publications appear in premier journals such as Duke Mathematical Journal, Compositio Mathematica, and Selecta Mathematica, reflecting significant contributions to the field.