Curriculum Vitae

Here's a PDF version of my CV.

Asher Auel

Gibbs Assistant Professor (Postdoc)

Department of Mathematics
Yale University
10 Hillhouse Avenue
New Haven, CT 06511

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

Born: 1981, Oregon (US citizen)
Languages: English (native), French (fluent), Hebrew (working).
Programming: HTML/CSS, LaTeX, Maple, Magma, GAP, C.

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)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

2013 - present Department of Mathematics, Yale University, New Haven, CT, USA
Gibbs Assistant Professor and 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)

Federal Grants

2016-2018 NSA Young Investigator Grant (PI)
$39,339, H98230-16-1-0321, "Azumaya algebras and rationality"
October 2016-December 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

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

Papers/Preprints

2017 Stable rationality of quadric and cubic surface bundle fourfolds
(with Christian Boehning and Alena Pirutka), submitted (27 pp.)
PDF   arXiv
2017 Failure of the local-global principle for isotropy of quadratic forms over rational function fields
(with V. Suresh), preprint (7 pp.)
PDF   arXiv
2017 Period-index bounds for arithmetic threefolds
(with Benjamin Antieau, Colin Ingalls, Daniel Krashen, Max Lieblich), preprint (17 pp.)
PDF   arXiv
2017 Some non-special cubic fourfolds
(with Nick Addington), preprint (13 pp.)
PDF   arXiv
2016 Conic bundles over threefolds with nontrivial unramified Brauer group
(with Christian Boehning, Hans-Christian Graf von Bothmer, and Alena Pirutka), preprint (37 pp.)
PDF   arXiv
2016 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
2015 Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
(with Marcello Bernardara), accepted for publication in the Proceedings of the London Mathematical Society (62 pp.)
PDF   arXiv
2015 Azumaya algebras without involution
(with Uriya First and Ben Williams), accepted in the Journal of the European Mathematical Society (18 pp.)
PDF   arXiv
2016 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.
2015 Surjectivity of the total Clifford invariant and Brauer dimension
Journal of Algebra 443 (2015), pp. 395-421.
PDF   arXiv   DOI
2014 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.
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

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.

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)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

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
2013 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

2015-2017 Senior essay advisor: helped shape an expositional/research project for two undergraduate math majors at 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 II 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.

Service/Outreach

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.
2015-2017 Yale Mathematics Department Algebra Qualifying Exam Board
2014-2015 Yale Mathematics Department Graduate Admissions Committee (co-chair)
2014-2015 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, Algebra and Number Theory, Algebraic Geometry, Journal für die reine und angewandte Mathematik, Geometriae Dedicata, Indian Journal of Pure and Applied Mathematics, International Mathematics Research Notices, Journal of Algebraic Geometry, Journal of K-theory, Journal of Pure and Applied Algebra, Linear Algebra and Applications, Mathematische Zeitschrift, Michigan Mathematical Journal, Pacific Journal of Mathematics, Proceedings of Edinburgh Mathematical Society, Proceedings of the AMS, Research in the Mathematical Sciences, and various conference proceedings volumes.

Graphic Design

2016 Breaking Enigma the first time, by David Saltman, undergraduate colloquium talk at Yale
2016 Algebraic Geometry Northeastern Series (AGNES) Spring 2016 at Yale
2015 Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE) mini-conference poster
2014 Bi-annual Algebraic and Tropical Meetings of Brown and YaLE (BATMOBYLE) mini-conference poster
2013 Colors of Math movie screening poster
2012 Cubic Surfaces, 27 Lines, and Icosehedra by Marcello Bernardara, undergraduate lecture poster
2011 Ramification in Algebra and Geometry (RAGE) conference poster

Research Seminar Organizing

2014-2017 Co-organizer of the Algebra and Number Theory Seminar, Yale University
2013-2017 Co-organizer of the Algebraic and Tropical Geometry Seminar, Yale University
2014-2017 Co-organizer of the Algebra and Lie Groups Seminar, Yale University
2012-2013 NYU local organizer for joint Columbia/CUNY/NYU RTG Number Theory Seminar

Conference/Workshop Organizing

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 on Varieties, 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

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

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 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