Asher Auel

Associate Professor

Department of Mathematics
Dartmouth College
6188 Kemeny Hall
27 N Main Street
Hanover, NH 03755

Email: asher * auel AT dartmouth * edu
Web: math.dartmouth.edu/~auel/

Education

2009 May	University of Pennsylvania, Philadelphia, Pennsylvania, USA Ph.D. Mathematics Ted Chinburg, Ph.D. dissertation adviser Title: Cohomological invariants of line bundle-valued quadratic forms Research areas: arithmetic geometry, quadratic forms, K-theory
2004 Jul	Université Paris-Sud XI Orsay, Paris, France Diplôme d'Études Approfondies (DEA) Mathématiques Pures Guy Henniart, DEA thesis adviser Title: Une démonstration d'un théorème de Bernstein sur les représentations de quasi-carré-intégrable de GLn(F) où F est un corps local non archimédien
2003 May	Reed College, Portland, Oregon, USA A.B. Mathematics Joe P. Buhler, undergraduate thesis adviser Title: Volumes of integer polynomials over local fields

Appointments

2021 -	Department of Mathematics, Dartmouth College, Hanover, NH, USA Associate Professor
2019 - 2021	Department of Mathematics, Dartmouth College, Hanover, NH, USA Assistant Professor
2014 - 2019	Department of Mathematics, Yale University, New Haven, CT, USA Gibbs Assistant Professor
2013 - 2014	Department of Mathematics, Yale University, New Haven, CT, USA Postdoctoral Associate
2012 - 2013	Courant Institute for Mathematical Sciences, New York University, New York, NY, USA NSF Postdoctoral Research Fellow (Sponsor: Yuri Tschinkel)
2010 - 2011	Max Planck Institute for Mathematics, Bonn, Germany Postdoctoral Fellow/Guest
2009 - 2012	Department of Mathematics and CS, Emory University, Atlanta, Georgia, USA NSF Postdoctoral Research Fellow (Sponsor: R. Parimala)

Grants

2022-2025	National Science Foundation Grant (PI) $360,000, DMS-2200845, "The algebra and arithmetic of splitting fields" August 2022-July 2025
2020-2025	Simons Foundation Collaboration Grant (PI) $42,000, 712097, "Geometry of splitting fields and rationality" September 2020-August 2025 (2022-2025 declined)
2016-2018	NSA Young Investigator Grant (PI) $39,339, H98230-16-1-0321, "Azumaya algebras and rationality" October 2016-September 2018
2013-2015	NSA Young Investigator Grant (PI) $39,755, H98230-13-1-0291, "Clifford algebras in arithmetic and geometry" August 2013-August 2015
2011	NSA Conference Grant (co-PI) $14,800, May 2011
2010-2011	NSF Conference Grant (co-PI) $24,295, DMS-1068423, May 2011
2009-2013	NSF Mathematical Sciences Postdoctoral Research Fellowship Scientific Sponsors: R. Parimala (Emory University), Yuri Tschinkel (Courant) $135,000, DMS-0903039, September 2009-July 2013

Academic Awards and Fellowships

2021 Nov	Senior Faculty Grant School of Arts and Sciences, Dartmouth College
2021 Jul	Susan and Gib Myers 1964 Faculty Fellowship School of Arts and Sciences, Dartmouth College
2019 Dec	Walter and Constance Burke Research Initiation Award School of Arts and Sciences, Dartmouth College
2008 Nov	Carlitz-Zippin Thesis Prize Mathematics Department, University of Pennsylvania
2008 Fall	School of Arts and Sciences Dissertation Completion Fellowship University of Pennsylvania
2004-2008	Calabi Fellow Mathematics Department, University of Pennsylvania
2003-2004	U.S. Advanced Student Fulbright Grant (France) Université Paris-Sud XI Orsay
2002-2003	Barry M. Goldwater Scholarship Reed College
2001-2003	James B. Small Scholarship Mathematics Department, Reed College
1998	Bronfman Youth Fellowship in Israel

Teaching Awards

2007	School of Arts and Sciences Award for Distinguished Teaching University of Pennsylvania
2007	Penn Prize for Excellence in Teaching by Graduate Students University of Pennsylvania
2005-2007	Good Teaching Award Mathematics Department, University of Pennsylvania

Books

2017	Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic (with B. Hassett, A. Várilly-Alvarado, and B. Viray eds.) Progress in Mathematics, Volume 320, Birkhäuser Basel, 2017. PUBLISHER

Papers/Preprints

2024	Distinguishing Brill-Noether loci (with Richard Haburcak and Andreas Leopold Knutsen), preprint arXiv:2406.19993, submitted (23 pp.) PDF   arXiv
2024	Failure of the local-global principle for isotropy of quadratic forms over function fields (with V. Suresh) accepted in Algebra and Number Theory (15 pp.) PDF   arXiv
2023	Maximal Brill-Noether loci via the gonality stratification (with Richard Haburcak and Hannah Larson), preprint arXiv:2310.09954 (12 pp.) PDF   arXiv
2023	Stickelberger’s discriminant theorem for algebras (with Owen Biesel and John Voight), American Mathematical Monthly 130 (2023), no. 7, pp. 656-670. PDF   arXiv   DOI
2023	A census of cubic fourfolds over F2 (with Avinash Kulkarni, Jack Petok, Jonah Weinbaum), submitted PDF   arXiv
2022	Maximal Brill-Noether loci via K3 surfaces (with Richard Haburcak), preprint arXiv:2206.04610 (33 pp.) PDF   arXiv
2021	Thinking about abstracts Notices of the American Mathematical Society 68, no. 10 (November 2021), pp. 1755-1756. DOI
2021	Explicit descent on elliptic curves and splitting Brauer classes (with Benjamin Antieau) preprint arXiv:2106.04291, submitted (31 pp.) PDF   arXiv
2020	Unramified Brauer groups of conic bundles threefolds in characteristic two (with Alessandro Bigazzi, Christian Boehning, and Hans-Christian Graf von Bothmer) American Journal of Mathematics 143 (2021), pp. 1601-1631. PDF   arXiv   DOI
2020	Brill-Noether special cubic fourfolds of discriminant 14 Facets of Algebraic Geometry: A Volume in Honour of William Fulton’s 80th Birthday, Volume 1 (editors Paolo Aluffi, David Anderson, Milena Hering, Mircea Mircea Mustață, Sam Payne), London Mathematical Society Lecture Note Series 472 (2022), Cambridge University Press, pp. 29--53. PDF   arXiv   DOI
2020	Conic bundles fourfolds with nontrivial unramified Brauer group (with Christian Boehning, Hans-Christian Graf von Bothmer, and Alena Pirutka) Journal of Algebraic Geometry 29 (2020), pp. 285-327. PDF   arXiv   DOI
2019	Universal triviality of the Chow group of 0-cycles and the Brauer group (with Alessandro Bigazzi, Christian Boehning, and Hans-Christian Graf von Bothmer) International Mathematics Research Notices, rnz171 (2019) PDF   arXiv   DOI
2019	The mathematics of Grace Murray Hopper Notices of the American Mathematical Society 66 (March 2019), pp. 330-340. DOI
2018	Period-index bounds for arithmetic threefolds (with Benjamin Antieau, Colin Ingalls, Daniel Krashen, Max Lieblich) Inventiones Mathematicae 26 (2019), no. 2, pp. 301-335. PDF   arXiv   DOI
2018	Azumaya algebras without involution (with Uriya First and Ben Williams) Journal of the European Mathematical Society 21 (2019), no. 3, pp. 897-921. PDF   arXiv   DOI
2018	Stable rationality of quadric and cubic surface bundle fourfolds (with Christian Boehning and Alena Pirutka) European Journal of Mathematics 4 (2018), no. 3, pp. 732-760. PDF   arXiv   DOI
2018	Some non-special cubic fourfolds (with Nick Addington) Documenta Mathematica 23 (2018), pp. 637-651. PDF   arXiv   DOI
2018	Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields (with Marcello Bernardara) Proceedings of the London Mathematical Society 117 (2018), no. 1, pp. 1-64 PDF   arXiv   DOI
2017	Cycles, derived categories, and rationality (with Marcello Bernardara) in Surveys on Recent Developments in Algebraic Geometry, Proceedings of Symposia in Pure Mathematics, vol. 95, Amer. Math. Soc., Providence, RI, 2017, pp. 199-266. PDF   arXiv   BOOK
2017	Universal unramified cohomology of cubic fourfolds containing a plane (with Jean-Louis Colliot-Thélène and R. Parimala) in Brauer Groups and Obstruction Problems: Moduli Spaces and Arithmetic, Progress in Mathematics, vol. 320, Birkhäuser Basel, 2017, pp. 29-56. PDF   arXiv   DOI
2015	Surjectivity of the total Clifford invariant and Brauer dimension Journal of Algebra 443 (2015), pp. 395-421. PDF   arXiv   DOI
2015	Quadric surface bundles over surfaces, (with R. Parimala and V. Suresh) Documenta Mathematica, Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015), pp. 31-70. PDF   arXiv   DOI
2014	Cubic fourfolds containing a plane and a quintic del Pezzo surface, (with Marcello Bernardara, Michele Bolognesi, and Anthony Várilly-Alvarado) Compositio Algebraic Geometry 1 (2014), issue 2, pp. 181-193. PDF   arXiv   DOI
2014	Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems, (with Marcello Bernardara and Michele Bolognesi) Journal de Mathématiques Pures et Appliquées 102 (2014), issue 1, pp. 249-291. PDF   arXiv   DOI
2013	Failure of the local-global principle for isotropy of quadratic forms over surfaces Quadratic Forms and Linear Algebraic Groups, Oberwolfach Reports 10 (2013), issue 2, report 31, pp. 1823--1825. PDF   DOI
2013	The transcendental lattice of the sextic Fermat surface (with Christian Boehning and Hans-Christian Graf von Bothmer) Mathematical Research Letters 20 (2013), no. 6, pp. 1017-1031. PDF   arXiv   DOI   Macauley2
2013	Exceptional collections of line bundles on projective homogeneous varieties, (with Alexey Ananyevskiy, Skip Garibaldi, and Kirill Zainoulline) Advances in Mathematics 236 (2013), pp. 111-130. PDF   arXiv   DOI
2013	Vector bundles of rank 4 and A3=D3, International Mathematical Research Notices 2013 (2013), no. 15, pp. 3450-3476. PDF   arXiv   DOI
2012	Remarks on the Milnor conjecture over schemes, Galois-Teichmüller Theory and Arithmetic Geometry (Kyoto, 2010), Advanced Studies in Pure Mathematics 63, 2012, pp. 1-30 PDF   arXiv   BOOK
2011	Clifford invariants of line bundle-valued quadratic forms, MPIM preprint series 2011 (33), 55 pp. PDF   MPIM
2011	Open problems on central simple algebras, (with Eric Brussel, Skip Garibaldi, Uzi Vishne) Transformation Groups 16, Issue 1 (2011), pp. 219-264. arXiv   DOI

Theses

2009	Cohomological invariants of line bundle-valued symmetric bilinear forms (Ph.D. thesis at the University of Pennsylvania, May 2009) with advisor Ted Chinburg) (submitted version, or the better single spaced version)
2004	Une démonstration d'un théorème de Bernstein sur les représentations de quasi-carré-intégrable de GLn(F) où F est un corps local non archimédien (DEA Thesis, Paris-Sud Orsay XI, July 2004), with advisor Guy Henniart (submitted [PDF])
2003	Volumes of integer polynomials over local fields (Undergraduate Thesis, Reed College, May 2003), with adviser Joe P. Buhler (submitted [PDF], with hi-resolution images)

Teaching

2022 Spring	Math 75 Applied Topics in Number Theory and Algebra: Mathematics of Cryptography Dartmouth College
2022 Winter	Math 125 Current Problems in Number Theory: Galois Cohomology and Descent (graduate course) Dartmouth College
2021 Fall	Math 71 Algebra Dartmouth College
2020 Fall	Math 101 Topics in Algebra: Quadratic Forms Dartmouth College
2020 Fall	Math 11 Accelerated Multivariable Calculus Dartmouth College
2020 Spring	Math 75 Applied Topics in Number Theory and Algebra: Mathematics of Cryptography Dartmouth College
2020 Winter	Math 81/111 Abstract Algebra (graduate course) Dartmouth College
2019 Fall	Math 11 Accelerated Multivariable Calculus Dartmouth College
2019 Spring	Math 373/573 Algebraic Number Theory (graduate course) Yale University
2019 Spring	Math 370 Fields and Galois Theory Yale University
2018 Fall	Math 608 Introduction to Arithmetic Geometry (graduate course) Yale University
2018 Spring	Math 225 Linear Algebra and Matrix Theory (two sections) Yale University
2018 Spring	Math 370 Fields and Galois Theory Yale University
2017 Fall	Math 115 Calculus of Functions of One Variable II (flipped classroom) Yale University
2017 Fall	Math 350 Introduction to Abstract Algebra Yale University
2017 Spring	Math 225 Linear Algebra and Matrix Theory Yale University
2016 Fall	Math 350 Introduction to Abstract Algebra Yale University
2016 Fall	Math 604 Introduction to Quadratic Forms (graduate course) Yale University
2016 Spring	Math 235 Reflection Groups Yale University
2016 Spring	Math 608 Introduction to Arithmetic Geometry (graduate course) Yale University
2015 Fall	Math 350 Introduction to Abstract Algebra Yale University
2015 Spring	Math 612 Arithmetic and Geometry of Linear Algebraic Groups (graduate course) Yale University
2015 Spring	Math 225 Linear Algebra and Matrix Theory Yale University
2014 Fall	Math 115 Calculus of Functions of One Variable II (flipped classroom) Yale University
2014 Spring	Math 225 Linear Algebra and Matrix Theory Yale University
2013 Fall	Math 115 Calculus of Functions of One Variable II Yale University
2012 Fall	Math 121 Calculus I Courant Institute of Mathematical Sciences, New York University
2012 Spr	Global Class Field Theory (graduate learning seminar) Emory University
2012 Spr	Math 211 Multivariable Calculus Emory University
2011 Fall	Math 211 Multivariable Calculus Emory University
2010 Spr	Math 211 Multivariable Calculus Emory University
2007 Sum	Ideas in Mathematics, topics in graph theory, history of mathematics, tilings and symmetries, and sudoku University of Pennsylvania
2006 Sum	Ideas in Mathematics, mathematical logic and foundations. University of Pennsylvania
2006-2007	Math 370-271 Abstract Algebra I and II (Teaching Assistant) University of Pennsylvania
2006 Spr	Math 203 Proving Things (Algebra) (Teaching Assistant) University of Pennsylvania
2005 Fall	Math 104 Calculus I (Teaching Assistant) University of Pennsylvania
2004-2005	Sunday Math Review (Review Leader) University of Pennsylvania
2002-2003	Paper Grader for Calculus, Abstract Algebra Reed College
2001-2003	Math Review Center (Review Leader) Reed College

Mentoring

2022-	Senior undergraduate thesis advisor: Athina Avrantini (2022-2023, will be PhD student at UPenn) Jonah Weinbaum (2022-2023, will be MA student in CS at Dartmouth)
2022-	Potdoc Mentor: Sarah Frei (John Wesley Young Research Instructor)
2021-	Potdoc Mentor: Jack Petok (lecturer)
2020-	Faculty advisor for the Directed Reading Program at Dartmouth. News publicity.
2020-	PhD Advisor: Richard Haburcak (5rd year student)
2020-	Premajor Advisor for first year undergraduate students at Dartmouth College.
2018-2019	Graduate student advisor in Yale Emerging Scholars Initiative Post-baccalaureate Research Education Program (ESI PREP): Andres Mejia
2015-2018	Senior undergraduate research project advisor at Yale: Claire Thompson (Spring 2019, now on Wall Street) Connor Halleck-Dube (Fall 2018, now Ph.D. student at Berkeley) Elijah Gunther (Spring 2018, now Ph.D. student at UPenn) Stanislav Atanasov (Spring 2017, now Ph.D. student at Columbia) Louis Gaudet (Fall 2015, now Ph.D. student at Rutgers)
2016-2018	Academic advisor for undergraduate mathematics majors at Yale.
2018-2019	Academic advisor for first year female STEM-interested students at Grace Hopper College, Yale.
2015 Mar	Study group leader for graduate students learning about K3 surfaces during the Arizona Winter School 2015.
2014-2016	Co-organized learning seminar for graduate students to prepare for talks in Yale’s Algebraic and Tropical Geometry seminar
2013 Feb	Mock orals chair for graduate student at Courant Institute, New York University
2006-2008	Member of the Penn Mathematics Department Master TA Program, responsible for organizing a week long teacher training program in the Fall and conduct long-term evaluation of incoming graduate students.
2001, 2003	Type I Wildland Firefighter (Squad Boss), Eagle Pass Reforestation Inc., Jacksonville, OR. Responsible for safety and personnel management of a 20 person hand crew during summer wildland fire seasons.

Outreach

2019	Participation in What's the Big Idea?, outreach program connecting classrooms to researchers through video interviews, Hanover, NH
2017	Participation in Synapse Resonance, an outreach program of the Yale Scientific Magazine aimed at high school students interested in STEM fields.
2016	Participation in Math Mornings , a series of public lectures aimed at middle school students interested in math. Article about event, where I am quoted.
2016-17	Participation in Iota, named for the inclusion map, which is a group of undergraduate math majors concerned with issues of diversity and inclusion in the Yale Mathematics Department. Consulted with the group about the creation of a peer-tutoring program for upper level math courses.
2015	Participated in organization of Art of the Equation, exhibition of prints and public lecture with David Mumford at the Yale University Art Gallery. Presented about mathematicians and chalk. Covered in Scientific American Blog and in David Mumford's blog.
2014	Participated in Pathways to Science Café, a high school science outreach program in New Haven, CT.
2013 Nov	Organized movie screening of Colors of Math including a conversation with executive producer Yuri Tschinkel at Yale Humanities Center.

Service

2021-2022	Graduate Recruiting Chair, Dartmouth College Mathematics Department
2021-2022	Tenure Track Recruitment Committee, Dartmouth College Mathematics Department
2020-2021	Selection Committee, Biographies of Contemporary Women in Mathematics, Dartmouth College Mathematics Department
2020-	Ad-Hoc Preliminary Exam Committee, Dartmouth College Mathematics Department
2020-2022	Graduate Admissions Committee, Dartmouth College Mathematics Department
2019-2022	Recruitment Committee, Dartmouth College Mathematics Department
2015-2017	Yale Mathematics Department Algebra Qualifying Exam Board
2014-2015	Yale Mathematics Department Graduate Admissions Committee (co-chair)
2014-2018	Yale Mathematics Department Website Committee (chair)
2013 Sep	Organized academic jobs information session and panel for graduate students, Yale University
2011-	Zentralblatt MATH reviewer
2009 Jan	Chaired AMS Session on Number Theory, III, at the Joint Mathematics Meetings, Wednesday, January 7th, 2009, together with Emma Previato.
2007-2008	Member of a graduate student committee (together with Andrew Obus and Shea Vela-Vick) spearheading the development of an honors calculus course, Math 116/260, to be first offered at Penn in Fall 2008.
2004-2008	Bicycle Mechanic Volunteer Facilitator, Neighborhood Bicycle Works, Philadelphia, PA. A nonprofit educational organization that seeks to increase opportunities for urban youth through bicycling.

Editorial Work

Referee for Advances in Applied Clifford Algebras, Advances in Geometry, Advances in Mathematics, Algebra and Number Theory, Algebraic Geometry, American Journal of Mathematics, Annals of K-Theory, Annales de l’institut Fourier, Annali della Scuola Normale Superiore di Pisa, Acta Mathematica, Bulletin des Sciences Mathéematiques, Canadian Journal of Mathematics, Canadian Mathematical Bulletin, Communications in Algebra, Compositio Mathematica, Comptes Rendus de l'Académie des Sciences Mathématique, Documenta Mathematica, Duke Mathematical Journal, Expositiones Mathematicae, Forum Mathematicum, Geometriae Dedicata, Geometry and Topology, Glasnik Matematicki, Indian Journal of Pure and Applied Mathematics, International Mathematics Research Notices, Inventiones mathematicae, Journal de l’Ecole Polytéchnique, Journal de Théorie des Nombres de Bordeaux, Journal für die reine und angewandte Mathematik, Journal of Algebraic Geometry, Journal of the AMS, Journal of the Australian Mathematical Society, Journal of K-theory, Journal of Pure and Applied Algebra, Linear Algebra and Applications, Manuscripta Mathematica, Mathematische Nachrichten, Mathematische Zeitschrift, Michigan Mathematical Journal, Notices of the American Mathematical Society, Pacific Journal of Mathematics, Proceedings of Edinburgh Mathematical Society, Proceedings of the London Mathematical Society, Proceedings of the AMS, Rendiconti Padova, Research in the Mathematical Sciences, Revista Matematica Complutense, Rocky Mountain Journal of Mathematics, Transactions of the AMS, and various conference proceedings volumes.

Graphic Design

2018	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 29
2017	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 30
2016	Breaking Enigma the first time, undergraduate colloquium talk by David Saltman about the history of the Enigma cipher machines used by the German Armed Forces during World War II, Yale University, September 28
2016	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, April 28
2016	Algebraic Geometry Northeastern Series (AGNES) Spring 2016 at Yale University, April 8-10
2015	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, December 10
2014	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 20
2013	Colors of Math, movie (by Ekaterina Eremenko) screening at Yale University, November 21, with executive producer Yuri Tschinkel
2012	Cubic Surfaces, 27 Lines, and Icosehedra, Courant Institute for Mathematical Sciences, New York University, November 7, undergraduate lecture by Marcello Bernardara about cubic surfaces, icosehedra, and linear perspective in 14th century Italian art
2011	Ramification in Algebra and Geometry (RAGE), Emory University, May 16-20

Research Seminar Organizing

2019-	Co-organizer of the Algebra and Number Theory Seminar, Dartmouth College
2013-2018	Co-organizer of the Algebraic and Tropical Geometry Seminar, Yale University
2014-2018	Co-organizer of the Algebra and Lie Groups Seminar, Yale University
2014-2018	Co-organizer of the Algebra and Number Theory Seminar, Yale University
2012-2013	NYU local organizer for joint Columbia/CUNY/NYU RTG Number Theory Seminar

Conference Series Organizational Committee

2017-	Algebraic Geometry Northeastern Series (AGNES)
2020-	Bi-annual Algebraic and Tropical Meetings of Brown and Institutions Located in its Environs (BATMOBILE)
2014-2020	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE)

Conference/Workshop Organizing

2022	Bi-annual Algebraic and Tropical Meetings of Brown and Institutions Located in its Environs (BATMOBILE), Amherst College, September 30, 2022.
2019	New Facets (early career workshop preceeding Facets of Algebraic Geometry conference), University of Michigan, Ann Arbor, October 18, with Melody Chan, Tyler Foster, and Milena Hering.
2018	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 29, 2018, with Kalina Mincheva and Yuchen Liu.
2018	Birational Geometry and Arithmetic, Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, RI, May 14-18, with Marta Pieropan, Sho Tanimoto, Yuri Tschinkel, Anthony Várilly-Alvarado.
2017	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 30, 2017, with Max Kutler, Yuchen Liu, Sam Payne.
2016	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, April 28, 2016, with Angie Cueto, José González, and Sam Payne.
2016	Algebraic Geometry Northeastern Series (AGNES), Yale University, April 8-10, 2016, with José González and Sam Payne.
2015	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, December 10, 2015, with Angie Cueto, José González, and Sam Payne.
2015	Rational points/Pontos racionais, Special Thematic Trimester in Algebraic Geometry, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brazil, May 25-29, 2015, with Cecília Salgado and Anthony Várilly-Alvarado
2015	Special Session on Quadratic Forms in Arithmetic and Geometry, AMS Spring Southeastern Sectional Meeting, University of Alabama in Huntsville, Huntsville, AL, March 27-29, 2015, with Jorge Morales and Anne Quéguiner-Mathieu
2014	Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Yale University, November 20, 2014, with Angie Cueto, José González, Nathan Kaplan, and Sam Payne.
2014	Special Session on Exceptional Groups in Physics, Algebra, and Geometry, AMS Fall Southeastern Sectional Meeting, University of North Carolina at Greensboro, Greensboro, NC, November 8-9, 2014, with Anthony Ruozzi and George McNinch
2014-2016	The geometry of Azumaya algebras in dimension 3, SQuaREs (Structured Quartet Research Ensembles), American Institute of Mathematics, July 21-25, 2014, with Ben Antieau, Colin Ingalls, Danny Krashen, and Max Lieblich
2013	Brauer groups and obstruction problems: moduli spaces and arithmetic at American Institute of Mathematics, Feb 25-Mar 1, 2013, with Brendan Hassett, Tony Várilly-Alvarado, and Bianca Viray
2013	AWM-AMS Special Session on The Brauer Group in Algebra and Geometry, Joint Mathematics Meetings, San Diego, California, January 9-12, 2013 with Kelly McKinnie and V. Suresh
2011	Ramification in Algebra and Geometry at Emory University, May 16-20 2011, with Eric Brussel, Skip Garibaldi, Daniel Krashen, and R. Parimala Funding: DMS-1068423, $24,295 (co-PI) and NSA conference grant, $14,800 (co-PI)

Workshops Attended/Visits

2024	K3 surfaces Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island, February 14-17.
2024	Shimura curves in the LMFDB Dartmouth College, Hanover, New Hampshire, February 5-9.
2023	AGNES @ UPenn University of Pennsylvania, October 13-15.
2023	Homemade Algebraic Geometry University of Alcalá, Alcalá de Henares, Spain, July 10-13.
2023	Institut Montpelliérain Alexander Grothendieck Visiting Michele Bolognesi, Montpellier, France, June 10-16.
2023	Institut de Mathématiques Visiting Marcello Bernardara, Toulouse, France, June 3-10.
2023	Hilbert schemes, moduli spaces, and symplectic varieties University of Nantes, France, May 31-June 2.
2023	Hilbert modular forms infrastructure week Dartmouth College, Hanover, New Hampshire, May 8-12.
2023	AGNES @ Stony Brook Simons Center for Geometry and Physics, Stony Brook University, April 28-30.
2023	Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting Simons Foundation Center, New York, NY, January 11-12.
2022	Hilbert modular forms infrastructure week Dartmouth College, Hanover, New Hampshire, December 12-16.
2022	AGNES @ Amherst UMass Amherst, November 18-20.
2022	Arithmetic Aspects of Algebraic Groups Banff International Research Station, Alberta, Canada, June 12-15.
2022	AGNES @ Rutgers Rutgers University (virtual), May 20-21.
2020	AGNES @ Stony Brook Stony Brook University (virtual), October 23-25.
2019	Workshop on Rationality Problems in Algebraic Geometry American Institute of Mathematics, San Jose, CA, July 29-August 2.
2018	Affine Algebraic Groups, Motives and Cohomological Invariants Banff International Research Station, Alberta, Canada, September 16-21.
2018	Classical Algebraic Geometry Mathematisches Forschungsinstitut Oberwolfach, Black Forest, Germany, July 15--21.
2018	Institut de Mathématiques Visiting Marcello Bernardara, Toulouse, France, July 10-14.
2018	Birational Geometry and Arithmetic Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, RI, May 14-18.
2018	AGNES @ Rutgers 2018 Rutgers University, New Brunswick, NJ, April 13-15.
2018	Quadratic Forms in Chile 2018 Summer School: Quadratic forms over function fields Universidad de Santiago de Chile, Santiago, Chile, January 2-5.
2017	AGNES @ Northeastern 2017 Northeastern University, Boston, MA, October 13-15.
2017	Simons Conference on Birational Geometry Simons Foundation Center, New York, NY, August 21-25.
2017	ALGAR 2017: Quadratic Forms and Local-Global Principles, University of Antwerp, Belgium, July 3-7.
2017	AGNES @ Stony Brook 2017 Stony Brook University, Stony Brook, NY, April 21-23.
2017	New Trends in Arithmetic and Geometry of Algebraic Surfaces Banff International Research Station, Alberta, Canada, March 12-17.
2016	AGNES @ UMass Amherst 2016 University of Massachusetts, Amherst, MA, November 4-6.
2016	Alberta British Columbia (ABC) Algebra Workshop University of Alberta, Edmonton, Alberta, Canada, October 29-31.
2016	Interacting Algebraic Geometry Institute de Mathématiques de Bourgogne, University of Burgundy, Dijon, France, July 4-8.
2016	New methods in birational geometry International Centre for Mathematics and Computer Science (CIMI), University of Toulouse, France, June 27-July 1.
2016	Birational geometry and reduction to positive characteristic Edge Days, University of Edinburgh, Scotland, UK, June 3-5.
2016	Geometry over nonclosed fields Simons Symposium, Schloss Elmau, Bavaria, Germany, April 17-23.
2016	AGNES @ Yale University 2016 Yale University, New Haven, CT, April 8-10.
2016	Unramified cohomology, derived categories, and rationality FRG Mini-Workshop, University of Utah, Salt Lake City, UT, February 26-28.
2015	AGNES @ Brown University 2015 Brown University, Providence, RI, October 2-4.
2015	Local-Global Principles and Their Obstructions FRG Workshop, University of Pennsylvania, Philadelphia, PA, October 1-3.
2015	The Use of Linear Algebraic Groups in Geometry and Number Theory Banff International Research Station, Alberta, Canada, September 13-18.
2015	AMS Summer Institute in Algebraic Geometry University of Utah, Salt Lake City, UT, July 27-31.
2015	Arizona Winter School 2015: Arithmetic and Higher-Dimensional Varieties University of Arizona, Tucson, March 14-18.
2015	Algebra/Algebraic Geometry Group University of Michigan, Ann Arbor, February 2-6, visiting Bill Fulton.
2014	The geometry of Azumaya algebras in dimension 3 American Institute of Mathematics, Palo Alto, CA, July 21-25.
2014	Workshop on Tropical Foundations Yale Univesity, New Haven, CT, May 11-14.
2014	AGNES @ Penn 2014 University of Pennsylvania, Philadelphia, PA, October 31-November 2.
2013	Quadratic Forms and Linear Algebraic Groups Worshop Mathematisches Forschungsinstitut Oberwolfach, Black Forest, Germany, June 16--22.
2013	Spring School and Workshop on Torsors, Motives and Cohomological Invariants Fields Institute, Toronto, Ontario, Canada, May 14--17.
2013	AGNES @ Yale 2013 Yale University, New Haven, CT, April 19-21.
2013	Brauer groups and obstruction problems: moduli spaces and arithmetic American Institute of Mathematics, Palo Alto, CA, February 25 - March 1.
2012	Arizona Winter School 2012: Ramification in Geometry Mathematics Department, University of Arizona, March 10-14.
2011	IRMAR algebraic geometry group visitor Université de Rennes 1, France, June 13-17, visiting Michele Bolognesi.
2011	Institut de Mathématiques de Bordeaux number theory group (A2X) visiter Université Bordeaux I, June 6-10, visiting Philippe Cassou-Noguès.
2011	Ramification in Algebra and Geometry Emory University, Atlanta, GA, May 16-20
2011	Forschungsinstitut für Mathematik guest researcher Eidgenössische Technische Hochschule, Zürich, Switzerland, May 2-6, visiting Max-Albert Knus.
2011	Progrès récents en théorie des modules galoisiens Centre International de Rencontres Mathématiques, Luminy, Marseilles, France, March 21-25.
2010	RIMS-Camp-Style Seminar: Galois-theoretic Arithmetic Geometry, International Institute for Advanced Studies, Kyoto, Japan, October 19-24.
2010	Lens Mini-Course 2010 Linear Algebraic Groups and Quadratic Forms: Patching, Involutions, and Buildings Université d'Artois, Lens, France, June 14-18.
2010	The Brauer Group in Israel Kibbutz Ketura, Israel, January 3-11.
2009	Non-Abelian Fundamental Groups in Arithmetic Geometry Final Workshop, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, December 14-18.
2009	Linear Algebraic Groups and Related Structures Banff International Research Station, Alberta, Canada, September 13-18 .
2009	Arizona Winter School 2009: Quadratic Forms Southwest Center for Arithmetic Geometry, University of Arizona, March 14-18. Full funding to attend.
2008	MIMS short-term visitor School of Mathematics, University of Manchester, May 7-June 6, visiting Martin Taylor
2008	IMB Number Theory Group (A2X) research visiter Institut de Mathématiques de Bordeaux, Université Bordeaux I, May 19-25, visiting Philippe Cassou-Noguès
2007	Fields Institute Summer School in Iwasawa Theory Mathematics Department, McMaster University, August 9-13. Full funding to attend.
2007	Arizona Winter School 2007: p-adic geometry Mathematics Department, University of Arizona, March 10-14. Full funding to attend.
2006	Clay Mathematics Institute 2006 Summer School: Arithmetic Geometry Mathematisches Institut, Georg-August-Universität, Göttingen, July 17-August 11. Full funding to attend.

Talks

2023 Dec	Recent advances in the period-index problem Algebraic Geometry Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY
2023 Oct	Recent advances in the period-index problem Algebra and Number Theory Seminar, Dartmouth College, Hanover, NH
2023 Sep	The local-global principle for quadratic forms over function fields III Algebra and Number Theory Seminar, Dartmouth College, Hanover, NH
2023 Jun	Maximal Brill-Noether loci Complex Geometry Seminar, Institut de Mathématiques de Toulouse, Université Paul Sabatier, France
2023 Apr	Maximal Brill-Noether loci Algebraic Geometry Seminar, Northwestern University, Evanston, IL
2023 Apr	A survey of cubic fourfolds over F2 Algebra and Number Theory Seminar, Dartmouth College
2023 Feb	Maximal Brill-Noether loci Harvard-MIT Algebraic Geometry Seminar, Harvard University, Boston, MA
2023 Feb	Brauer classes split by genus one curves Algebra, Geometry, and Number Theory Seminar, Tufts University, Boston, MA
2022 May	Unramified cohomology of products of elliptic curves Algebra and Number Theory Seminar, Dartmouth College
2022 Jan	Brauer classes split by genus one curves QFLAG: Quadratic forms, Linear algebraic groups and Beyond (virtual)
2021 Nov	Recent breakthroughs in the rationality problem Colloquium, Rice University, Houston (virtual)
2021 Apr	Brill--Noether theory for cubic fourfolds Hodge seminar, University of Edinburgh, UK (virtual)
2021 Apr	Brauer classes split by genus one curves Quebec-Vermont Number Theory Seminar, Quebec City/Montreal/Burlington (virtual)
2021 Mar	The local-global principle for quadratic forms over function fields Number Theory and Algebraic Geometry Seminar, Simon Fraser University, British Columbia, Canada (virtual)
2021 Feb	Brill-Noether theory for cubic fourfolds Algebraic Geometry Seminar, University of Warwick, UK (virtual)
2021 Jan	The local-global principle for quadratic forms over function fields II Algebra and Number Theory Seminar, Dartmouth College (virtual)
2021 Jan	The local-global principle for quadratic forms over function fields Joint Mathematics Meetings, AMS Special Session on Galois Cohomology in Arithmetic Geometry (virtual)
2020 Oct	Sextic normal genus one curves Algebra and Number Theory Seminar, Dartmouth College (virtual)
2020 Oct	Brill-Noether special cubic fourfolds Special Session on Geometry and Arithmetic of Hyperkähler Manifolds, Fall Southeastern AMS Sectional Meeting, University of Tennessee, Chattanooga (virtual)
2020 June	Elliptic curves and the local-global principle for quadratic forms Connecticut Summer School in Number Theory 2020 Conference, University of Connecticut, Storrs (virtual)
2020 May	The local-global principle for quadratic forms over function fields Séminaire Variétés Rationnelles, Sorbonne Université Jussieu, Paris
2019 Oct	Brauer classes split by genus one curves 2019 Maine/Québec Number Theory Conference, University of Maine, Orono
2019 Jul	Unramified cohomology and the specialization method American Institute of Mathematics, Workshop on Rationality Problems in Algebraic Geometry, July 29-August 2
2019 Apr	Torsors over moduli of genus one curves and splitting Brauer classes Algebraic Geometry Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY
2019 Jan	Quadratic forms in four variables Colloquium, Dartmouth College, Hanover, NH (poster)
2018 Sep	Isotropy of quadratic forms over function fields Affine Algebraic Groups, Motives and Cohomological Invariants, Banff International Research Station, Alberta, Canada
2018 May	Noether's problem Colloquium, Dartmouth College, Hanover, NH (poster)
2018 May	The local-global principle for quadratic forms over function fields Algebra and Number Theory Seminar, Dartmouth College, Hanover, NH
2018 May	The period-index problem for surfaces over a local field Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE), Massachusetts Institute of Technology, Boston, MA
2018 Mar	Noether's problem Colloquium, Reed College, Portland, OR
2018 Mar	Noether's problem Yale Undergraduate Math Society seminar, Yale University, New Haven, CT
2018 Feb	Rationality of two-three fourfolds Algebraic Geometry Seminar, Yale University, New Haven, CT
2018 Jan	A tale of two-three fourfolds Algebraic Geometry Seminar, University of Michigan, Ann Arbor, MI
2018 Jan	Quadratic forms over function fields of complex curves and surfaces (3 lecture series) Quadratic forms in Chile 2018 Summer School: Quadratic forms over function fields, Universidad de Santiago de Chile, Santiago, Chile
2017 Dec	The local-global principle for isotropy over function fields Algebra seminar, University of Pennsylvania, Philadelphia, PA
2017 Dec	Platonic solids (Tedx Yale) Synapse Resonance, Outreach program of the Yale Scientific Magazine, New Haven, CT
2017 Oct	The local-global dimension spectrum of quadratic forms Algebraic Geometry Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY
2017 Aug	Segre fourfold and sextic del Pezzo fibrations Simons Conference on Birational Geometry, New York, NY
2017 Jul	Local-global principles in number theory and geometry (3 talk lecture series) ALGAR 2017: Quadratic Forms and Local-Global Principles, University of Antwerp, Belgium
2017 Mar	Geometry via counting points Colloquium, Center for Communications Research, Princeton, NJ
2017 Mar	Decomposition of the diagonal and phantom categories on surfaces New Trends in Arithmetic and Geometry of Algebraic Surfaces, Banff International Research Station, Alberta, Canada
2016 Nov	Stable rationality of conic bundle fourfolds AGNES Fall 2016, University of Massachusetts, Amherst, MA
2016 Oct	The torsion order of an algebraic variety Algebraic Geometry Seminar, University of British Columbia, Vancouver, Canada
2016 Oct	Stable rationality of conic bundle fourfolds Alberta British Columbia (ABC) Algebra Workshop University of Alberta, Edmonton, Alberta, Canada
2016 Oct	Platonic solids and symmetry Math Mornings (public outreach lecture series), Yale University, New Haven, CT
2016 Oct	Packing in lattices Yale Undergraduate Mathematics Society, Yale University, New Haven, CT
2016 Jul	Torsion universal 0-cycles on fibrations Interacting Algebraic Geometry, Institute de Mathématiques de Bourgogne, University of Burgundy, Dijon, France
2016 Jun	The torsion order of an algebraic variety New methods in birational geometry, International Centre for Mathematics and Computer Science (CIMI), University of Toulouse, France
2016 Jun	Stable rationality of some fibrations Edge Days, Birational geometry and reduction to positive characteristic, University of Edinburgh, Scotland, UK
2016 Jun	Brill-Noether theory for cubic fourfolds Edge Algebra Seminar, University of Edinburgh, Scotland, UK
2016 Apr	Universal triviality of 0-cycles and the degeneration method Algebraic Geometry Seminar, University of Illinois, Chicago, IL
2016 Apr	Stable rationality of quadric bundles Simons Symposium, Geometry over nonclosed fields, Schloss Elmau, Bavaria, Germany Lecture notes
2016 Mar	Limits of pfaffian cubic fourfolds Algebraic Geometry Seminar, Courant Institute of Mathematical Sciences, New York University, New York, NY
2016 Feb	Rationality and 0-cycles & 0-cycles on cubics (two talk lecture series) FRG Mini-Workshop, Unramified cohomology, derived categories, and rationality, University of Utah, Salt Lake City, UT
2016 Jan	The rationality problem in algebraic geometry Colloquium, University of Connecticut, Storrs, CT
2015 Oct	Curves, K3 surfaces, and cubic fourfolds Algebra Seminar, University of Connecticut, Storrs, CT
2015 Oct	Local-global obstructions for quadrics over function fields Local-Global Principles and Their Obstructions, FRG Workshop, University of Pennsylvania, Philadelphia, PA
2015 Sep	Algebras of composite degree split by genus one curves The Use of Linear Algebraic Groups in Geometry and Number Theory, Banff International Research Station, Alberta, Canada
2015 Sep	Brill-Noether theory for cubic fourfolds Algebraic and Tropical Geometry Seminar, Yale Univeristy, New Haven, CT
2015 Jul	Brill-Noether special cubic fourfolds AMS Summer Institute in Algebraic Geometry, University of Utah, Salt Lake City, UT
2015 Apr	How to take the derivative of the Dirac delta function Yale Undergraduate Mathematics Society, Yale University, New Haven, CT
2015 Mar	On the Euclidean Division (on behalf of Eva Bayer) Invited Address, AMS Spring Southeastern Sectional Meeting, University of Alabama in Huntsville, AL
2015 Feb	Pfaffian cubic fourfolds and curves of genus 8 Algebraic Geometry Seminar, Stony Brook University, Stony Brook, NY
2015 Feb	Cycles on cubic fourfolds Algebraic Geometry Seminar, University of Michigan, Ann Arbor, MI
2015 Feb	Recent upsets in some rationality problems Colloquium, University of Michigan, Ann Arbor, MI
2014 Oct	Quadratic forms of low dimension Junior Colloquium, Yale University, New Haven, CT
2014 Oct	Pick's Theorem Pathways to Science Café, Yale University, New Haven, CT
2014 Sep	Points, lines, and surfaces in cubic fourfolds Valley Geometry Seminar, University of Massachussetts, Amherst, MA
2014 Sep	The geography of cubic fourfolds Secret Tropical and Algebraic Geometry Seminar, Yale University, New Haven, CT
2014 Jun	Crab puzzles on lattices Summer Undergraduate Mathematics Research at Yale (SUMRY) Colloquium, Yale University, New Haven, CT
2014 Apr	Points, lines, and conics Yale Undergraduate Math Society, Yale University, CT
2014 Mar	Azumaya algebras without involution Special Session on Galois Cohomology and the Brauer Group, AMS Southeastern Spring Sectional Meeting, University of Tennessee, Knoxville, TN
2014 Mar	Points and conics Math Club, University of Connecticut, Storrs, CT
2014 Feb	Central simple algebras in algebra and geometry I/II (series of two talks) Algebra and Lie Group Seminar, Yale University, New Haven, CT
2014 Jan	The rationality question for cubic fourfolds Algebra Seminar, University of Connecticut, Storrs, CT
2013 Oct	A game on the exceptional group G2 and a conjecture concerning flag varieties Algebra Seminar, Wesleyan University, Middletown, CT
2013 Sept	Three approaches to the rationality problem for cubic fourfolds Algebraic and Tropical Geometry Seminar, Yale University, New Haven, CT
2013 Jun	Failure of the local-global principle for isotropy of quadratic forms over surfaces Quadratic Forms and Linear Algebraic Groups, Oberwolfach, Germany
2013 May	Orthogonal group schemes with simple degeneration Spring School on Torsors, Fields Institute, Toronto, Ontario, Canada
2013 Apr	Unramified cohomology of cubic fourfolds Algebraic Geometry Seminar, Courant Institute, New York University, New York, NY
2013 Apr	Rational cubic fourfolds containing a plane Algebraic Geometry Seminar, Brown University, Providence, RI
2013 Feb	Cubic fourfolds containing a plane and a quartic scroll Algebraic Geometry Seminar, Columbia University, New York, NY
2013 Feb	Quaternions over quadratic rings and quaternary quadratic forms Number Theory Seminar, MIT, Boston, MA
2013 Feb	Introduction to p-adic Hodge theory (two 1.5 hour talks) Lucien Szpiro's Impromptu Seminar, CUNY Graduate Center, New York, NY
2013 Feb	Exceptional collections of line bundles on projective homogeneous G2-varieties Algebraic Geometry Seminar, Courant Institute, New York University, New York, NY
2013 Jan	The anabelian conjectures for proper p-adic curves (d'après Mochizuki) Lucien Szpiro's Impromptu Seminar, CUNY Graduate Center, New York, NY
2013 Jan	Quadric surface bundles and quaternion algebras AMS Special Session on Number Theory and Geometry, Joint Mathematics Meeting, San Diega, CA
2012 Oct	Nontrivial rational cubic fourfolds containing a plane Algebra Seminar, University of Pennsylvania, Philadelphia, PA
2012 Sep	Quadric surface bundles and quaternion algebras over surfaces Algebraic Geometry Seminar, Courant Institute, New York University, New York, NY
2012 May	Quadric surface bundles over surfaces Algebra Seminar, University of Pennsylvania, Philadelphia, PA
2012 Mar	Fröhlich twisting via orthogonal motives Special Session on Hopf Algebras and Galois Module Theory, 2012 Spring Southeastern Section Meeting, University of South Florida, Tampa, March 10-11
2011 Oct	Rationality of families of intersections of quadrics and derived categories Algebraic Geometry seminar, Rice University, Houston, TX
2011 Aug	Pascal's rule for vector bundles of rank 4 Algebra and Number Theory seminar, Emory University, Atlanta, GA
2011 Jun	Quadratic forms over curves Number theory seminar, Technische Universität Dortmund, Germany
2011 Jun	Rationalité des cubiques de dimension quatre et algèbres de Clifford Algebraic geometry seminar, Université de Rennes 1, France
2011 Jun	Les invariants de Clifford-Hasse-Witt sur les courbes p-adiques et les surfaces sur les corps finis Number theory seminar, Université de Bordeaux 1, France
2011 Jun	Décomposition motivique des quadriques et des espaces homogènes projectifs Groupe de travail Géométrie Algébrique et Géométrie Arithmétique (GAGA), Université de Bordeaux 1, France
2011 June	Zéros des formes quadratiques sur les corps globaux Séminaire "Jouve-Pazuki", Université de Bordeaux 1, France
2011 Jan	Milnor's conjecture for p-adic curves Number theory lunch seminar, Max-Planck-Institut für Mathematik, Bonn, Germany
2010 Dec	Decompositions of rank four vector bundles Oberseminar, Universität Duisburg-Essen, Essen, Germany
2010 Dec	Rank four vector bundles on four-folds and "exceptional" isomorphisms of linear algebraic groups The MAThematics Center Heidelberg (MATCH), Faculty of Mathematics and Computer Sciences, Universität Heidelberg, Germany
2010 Nov	Rank four vector bundles on fourfolds Seminar Algebraic Geometry (SAG), Universität Bonn, Germany
2010 Oct	A Milnor conjecture for p-adic curves RIMS-Camp-Style seminar Galois-theoretic Arithmetic Geometry, International Institute for Advanced Studies, Kyoto, Japan
2010 Oct	A Milnor conjecture for p-adic curves Nachwuchskonferenz: Young Researchers in Arithmetic and Algebraic Geometry, Johannes Gutenberg-Universität, Mainz, Germany
2010 Jun	Involutions on Clifford algebras of line bundle-valued quadratic forms Lens Mini-Course 2010, Université d'Artois, Lens, France
2010 Feb	Chow groups of quadrics I/II (two talks) Algebra Seminar, Emory University
2010 Jan	(Non-)surjectivity of the Clifford invariant Brauer Group in Israel, Kibbutz Ketura, Israel
2009 Nov	Essentially self-dual vector bundles on algebraic varieties Algebraic Geometry Seminar, Duke University, Durham, NC
2009 Nov	Quaternions and conic sections: from algebra to geometry Mathematics colloquium Wake Forest University, Winston-Salem, NC
2009 Oct	Clifford sequences in the theory of line bundle-valued quadratic forms over arithmetic schemes 2009 Fall Southeastern Meeting, Special Session on Arithmetic Geometry, Boca Raton, FL.
2009 Oct	Invariants of quadratic forms over algebraic varieties Number Theory Seminar, University of Georgia Athens
2009 Oct	Steenrod squares in Chow groups I/II (two talks) Algebra Seminar, Emory University
2009 Sep	A Clifford invariant for line bundle-valued quadratic forms LAG workshop, Banff International Research Station, Alberta, Canada.
2009 Sep	Mod 4 invariants of line bundle-valued quadratic forms Algebra Seminar, Emory University
2009 Jan	Characteristic classes and root numbers for motives associated to GOn Joint Mathematics Meetings 2009, Washington, DC
2008 Dec	Characteristic classes for essentially self-dual Galois representations Galois Seminar, University of Pennsylvania
2008 Nov	From quaternion algebras to conic sections Mathematics Colloquium, Reed College
2008 Nov	Cohomological invariants of line bundle-valued quadratic forms Number Theory Seminar, Mathematics Department, University of California San Diego
2008 Nov	Self-dual Galois representations Center for Communications Research (CCR) West, La Jolla, CA
2008 May	Invariants «modulo 4» de formes quadratiques à valeurs dans des fibres Graduate Student Number Theory Seminar, IMB Université Bordeaux I
2008 Mar	Theta divisors and fundamental groups of curves in characteristic p Galois Seminar, University of Pennsylvania
2008 Feb	Simple Values of Sine and Cosine Graduate Student Pizza Seminar, University of Pennsylvania
2007 Aug	Iwasawa theory over imaginary quadratic fields Fields Institute Summer School in Iwasawa Theory, McMaster University
2007 Apr	Orthogonal Galois theoretic characteristic classes I/II (two talks) Galois Seminar, University of Pennsylvania
2007 Feb	The co-site of modules over a non-commutative ring I/II (two talks) Graduate Student Non-Commutative Algebraic Geometry Seminar, University of Pennsylvania
2006 Nov	Abelian varieties: canonical maps and functorial characterizations Graduate Student Arithmetic Geometry Seminar, University of Pennsylvania
2006 Oct	Can the automorphism group of an infinite field be so large? Galois Seminar, University of Pennsylvania
2006 Sep	Abelian varieties over C Graduate Student Arithmetic Geometry Seminar, University of Pennsylvania
2006 Feb	Fields of moduli of 3-point covers with mild reduction, Galois Seminar, University of Pennsylvania
2005 Oct	An introduction to model theory Topics Course on Model Theory and Quadratic Forms, University of Pennsylvania
2005 Oct	A generating function of étale algebras over a local field Graduate Student Pizza Seminar, University of Pennsylvania
2005 Jun	Zapponi's work on the Galois action on diameter four trees I/II (two talks) Galois Seminar, University of Pennsylvania
2004 Oct	The probability that a p-adic polynomial splits Graduate Student Pizza Seminar, University of Pennsylvania
2004 Jan	Expose de courbes elliptiques sur C Course on Modular Forms and Modular Curves, Paris-Sud XI Orsay
2002 Dec	p-adic polynomials Mathematics Colloquium, Reed College
2002 Oct	Distributions: how to think about the Dirac δ-function Student Exposition Series, Reed College
2002 Feb	Classifying locally compact topological groups Student Exposition Series, Reed College