## Research Publications

**Local-Global Principles for Constant Reductive Groups over Semi-Global Fields**,
with J.-L. Colliot-Thelene, D. Harbater, J. Hartmann, R. Parimala and V. Suresh,
Michigan Mathematical Journal,
vol. 72 (August 2022), 77-144

**Bounding cohomology classes over semiglobal fields**,
with David Harbater and Julia Hartmann,
To appear in Israel Journal of Mathematics

**Local-Global Principles for Curves over Semi-Global Fields**,
with David Harbater and Alena Pirutka,
Bulletin of the London Mathematical Society,
53 (1), Feb. 2021, 177--193

**Local-Global Principles for Tori over Arithmetic Curves**,
with Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann, R. Parimala and V. Suresh,
Algebraic Geometry,
7 (5) (2020) 607--633

**Multiparty Non-Interactive Key Exchange and More From Isogenies on Elliptic Curves**,
with Dan Boneh, Darren Glass, Kristin Lauter, Shahed Sharif, Alice Silverberg, Mehdi Tibouchi and Mark Zhandry,
in the Journal of Mathematical Cryptology,
Vol. 14, no. 1 (2020)

**Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields**,
with Jean-Louis Colliot-Thélène, David Harbater, Julia Hartmann, R. Parimala and V. Suresh,
Transactions of the American Mathematical Society,
372 (2019), no. 8, 5263--5286

**Period-index bounds for arithmetic threefolds**,
with Benjamin Antieau, Asher Auel, Colin Ingalls and Max Lieblich,
Inventiones Mathematicae,
216 (2019), no. 2, 301-335

**Local-global Galois theory of arithmetic function fields**,
with David Harbater, Julia Hartmann, R. Parimala and V. Suresh,
Israel Journal of Mathematics,
vol. 232, no. 2 (2019), 849-882

**Derived categories for torsors for Abelian schemes**,
with Benjamin Antieau and Matthew Ward,
Advances in Mathematics,
306 (2017), 1-23

**Period and index, symbol lengths, and generic splittings in Galois cohomology**,
Bulletin of the London Mathematical Society,
48 (2016), no. 6, 985-1000

**Local-global principles for torsors over arithmetic curves**,
with David Harbater and Julia Hartmann,
American Journal of Mathematics,
137 (2015), no. 6, 1559--1612

**Diophantine and cohomological dimensions**,
with Eliyahu Matzri,
Proceedings of the AMS,
143 (2015), no. 7, 2779--2788

**Refinements to patching and applications to field invariants**,
with David Harbater and Julia Hartmann,
International Math. Research Notices,
doi: 10.1093/imrn/rnu278 (2015)

**Local-global principles for Galois cohomology**,
with David Harbater and Julia Hartmann,
Commentarii Mathematici Helvetici,
89 (2014), no. 1, 215--253

**Weierstrass preparation and algebraic invariants**,
with David Harbater and Julia Hartmann,
Mathematische Annalen,
356 (2013), no. 4, 1405--1424

**Relative Brauer groups of genus 1 curves**,
with Mirela Ciperiani,
Israel Journal of Mathematics,
192 (2012), no. 2, 921--949

**Appendix to: Period and index in the Brauer group of an arithmetic surface**,
by Max Lieblich,
Journal für die reine und angewandte Mathematik,
659 (2011), 1--41

**Patching subfields of division algebras**,
with David Harbater and Julia Hartmann,
Transactions of the American Mathematical Society,
363 (2011), no. 6, 3335--3349

**Distinguishing division algebras by finite splitting fields**,
with Kelly McKinnie,
Manuscripta Mathematica,
134 (2011), no. 1-2, 171--182

**Field patching, factorization, and local-global principles**,
Quadratic forms, linear algebraic groups, and cohomology,
57--82, Dev. Math., 18, Springer, New York, 2010

**Corestrictions of algebras and splitting fields**,
Transactions of the American Mathematical Society,
362 (2010), no. 9, 4781--4792

**Zero cycles on homogeneous varieties**,
Advances in Mathematics,
223 (2010), no. 6, 2022--2048

**Applications of patching to quadratic forms and central simple algebras**,
with David Harbater and Julia Hartmann,
Inventiones Mathematicae,
178 (2010), no. 2, 231--263

**Pointed trees of projective spaces.**,
with Linda Chen and Angela Gibney,
Journal of Algebraic Geometry,
18 (2009), no. 3, 477--509

**Index reduction for Brauer classes via stable sheaves**,
with Max Lieblich,
International Mathematics Research Notices,
no. 8 (2008), Art. ID rnn010, 31 pp

**Birational maps between generalized Severi-Brauer varieties**,
Journal of Pure Applied Algebra,
212 (2008), no. 4, 689--703

**Motives of unitary and orthogonal homogeneous varieties**,
Journal of Algebra,
318 (2007), no. 1, 135--139

**Severi-Brauer varieties and symmetric powers**,
with David J. Saltman,
Algebraic transformation groups and algebraic varieties,
59--70, Encyclopaedia Math. Sci., 132, Springer, Berlin, 2004

**Severi-Brauer varieties of semidirect product algebras**,
Documenta Mathematica,
8 (2003), 527--546 (electronic)