# Research

#### Publications

(with M. Ballard and A. Duncan) The toric Frobenius morphism and a conjecture of Orlov, 2017.

(with M. Ballard and A. Duncan) On derived categories of arithmetic toric varieties, 2017.

Zero-cycles with coefficients for the second generalized symplectic involution variety of an algebra of index 4, submitted, 2017.

K-Cohomology of Generalized Severi-Brauer Varieties. Ph.D. Thesis, University of Georgia (2016).

(with E. J. Rhodes, et al.) Temporal changes in the frequencies and widths of the solar p-mode oscillations. Proceedings of SOHO 24/GONG 2010, pp. 134-138 (2011).

(with E. J. Rhodes, et al.) Temporal changes in the frequencies of the solar p-mode oscillations during solar cycle 23. Proceedings of the IAU, Vol. 6, Symposium S273, pp. 389-393 (2011).

#### In-Progress

Patching over fields and étale K-theory.

The Chen-Gibney-Krashen moduli spaces revisited
(with P. Gallardo, N. Giansiracusa, and X. Wu).

A cocycle-free proof of a theorem of Uematsu on the Brauer group of affine diagonal quadrics
(with R. Gordon-Sarney, D. Adams, D. Litt, S. Mathur).

#### Expository Articles

Below is a collection of expositions derived from course assignments and selected talks.

Introduction to K3 surfaces.
K-theory of algebraic curves.

Compactifications of $M_{0,n}$ from rational normal curves.
Sheaf cohomology on a Grothendieck site.

Homotopical and homological algebra.
The Brauer group.

Grassmannians as moduli spaces.

#### Beamer Presentations

Chow Groups with Coefficients and Generalized Severi-Brauer Varieties.
Milnor-Witt Groups and Homotopy Theory of Schemes.

Twisted Homogeneous Varieties, Derived Equivalences, and dg-Stacks.
Subfields of Central Simple Algebras.

The Severi-Brauer Variety Associated to a Central Simple Algebra.
Spectra: A Home for Homology