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).
PDF


(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).
IOP

(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).
NSO


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.
pdf
K-theory of algebraic curves.
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Compactifications of $M_{0,n}$ from rational normal curves.
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Sheaf cohomology on a Grothendieck site.
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Homotopical and homological algebra.
pdf
The Brauer group.
pdf

Grassmannians as moduli spaces.
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Beamer Presentations


Chow Groups with Coefficients and Generalized Severi-Brauer Varieties.
pdf
Milnor-Witt Groups and Homotopy Theory of Schemes.
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Twisted Homogeneous Varieties, Derived Equivalences, and dg-Stacks.
pdf
Subfields of Central Simple Algebras.
pdf

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