## Publications

**Local-Global Principles for Tori over Arithmetic Curves**, with Jean-Louis Colliot-Th\'el\`ene, 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

**Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields**, with Jean-Louis Colliot-Th\'el\`ene, David Harbater, Julia Hartmann, R. Parimala and V. Suresh,
Trans. Amer. Math. Soc., 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,
Comment. Math. Helv., 89 (2014), no. 1, 215--253

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

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

**Appendix to: Period and index in the Brauer group of an arithmetic surface**
By Max Lieblich,
,
J. Reine Angew. Math., 659 (2011), 1--41

**Patching subfields of division algebras**, with David Harbater and Julia Hartmann,
Trans. Amer. Math. Soc., 363 (2011), no. 6, 3335--3349

**Distinguishing division algebras by finite splitting fields**, with Kelly McKinnie,
Manuscripta Math., 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**,
Trans. Amer. Math. Soc., 362 (2010), no. 9, 4781--4792

**Zero cycles on homogeneous varieties**,
Adv. Math., 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,
J. Algebraic Geom., 18 (2009), no. 3, 477--509

**Index reduction for Brauer classes via stable sheaves**, with Max Lieblich,
Int. Math. Res. Not. IMRN, no. 8 (2008), Art. ID rnn010, 31 pp

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

**Motives of unitary and orthogonal homogeneous varieties**,
J. 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**,
Doc. Math., 8 (2003), 527--546 (electronic)