Research

Papers and Preprints:

1. Finiteness of Tate-Shafarevich sets for non-commutative algebraic groups over function fields (In preparation)

 For some preliminary notes on this, see here. These are informal working notes and still very much in progress.

2. (with A.S. Rapinchuk and I. Rapinchuk) Product of trees and PGL_{2}-torsors over the punctured affine line, preprint (arXiv)

3. (with I. Rapinchuk) Finiteness of the Tate-Shafarevich group over function fields for groups of multiplicative type, preprint (arXiv)

Conference and Seminar Talks:

• Local-Global Principles and Tate Shafarevich groups over function fields, SERMON Conference, High Point University, April 12, 2026

• Brauer group of a local field and introduction to local class field theory, MSU Algebra Learning Seminar (Fall '25)

• Complex Elliptic Curves, MSU Algebra Learning Seminar (Spring '25)

• Galois cohomology and abstract Galois descent, MSU Student Algebra Seminar (Fall '24)

• Endomorphisms of complex elliptic curves, Algebra Learning Seminar on complex multiplication and Kronecker’s Jugendtraum (Spring '24)

• Elliptic functions and elliptic curves, Algebra Learning Seminar on complex multiplication and Kronecker’s Jugendtraum (Spring '24)

• What is a reciprocity law?, MSU Student Algebra Seminar (Spring '24)

• Homological characterization of Brauer groups, MSU Student Algebra Seminar (Fall '23)