Courses
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Princeton University
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Math 102, Calculus, Spring 1996 and Spring 1997.
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University of California, Berkeley
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Math 185, Complex analysis, Fall 1997.
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Math H1B, Honors calculus, Fall 1998.
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Math 256B, Algebraic geometry, Spring 1999.
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Math 254B, Number theory, Spring 2000.
- Math 54, Linear algebra and differential equations, Spring 2001.
- Math 55, Discrete mathematics, Fall 2001.
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Math 274, Rational points on varieties, Spring 2003.
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Math 250A, Groups, rings, and fields, Fall 2003.
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Math 140, Metric differential geometry, Spring 2004.
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Math 185, Complex analysis, Spring 2004.
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Math 160, History of mathematics, Spring 2005.
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Math 16A, Analytic geometry and calculus, Fall 2006.
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Institut Henri Poincaré
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Rational points on curves, during the "Explicit methods in number theory" trimester, Fall 2004.
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p-adic approaches to rational points on curves, during the "Reinventing rational points" trimester, April-July 2019.
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MIT
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18.821, Project laboratory in mathematics, Fall 2007,
with Susan Ruff and David Vogan.
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18.787, Rational points on varieties, Fall 2008.
- 18.02, Multivariable calculus, Fall 2009.
- 18.782, Introduction to arithmetic geometry (new course), Fall 2009.
- 18.02, Multivariable calculus, Fall 2010.
- 18.725, Algebraic Geometry I, Fall 2010.
- 18.725, Algebraic Geometry I, Fall 2011.
- 18.02, Multivariable calculus, Spring 2013.
- 18.726, Algebraic Geometry II, Spring 2013.
- 18.787, Rational points on varieties, Fall 2013.
- 18.03, Differential equations, Spring 2014 (received the MIT School of Science Prize in Undergraduate Teaching for this class).
- 18.099/18.999, Reading course on elliptic curves, Spring 2014.
- 18.785, Number Theory I, Fall 2014.
- 18.A34, Mathematical Problem Solving, Fall 2014.
- 18.786, Number Theory II, Spring 2015.
- 18.A34, Mathematical Problem Solving, Fall 2016.
- 18.715, Introduction to Representation Theory, Fall 2016.
- 18.117, Hodge theory, Spring 2017.
- 18.708, Topics in algebra (Drinfeld modules and explicit class field theory), May 9-18, 2017.
- 18.03, Differential equations, Spring 2018.
- 18.704, Seminar in algebra: finite groups, Fall 2018.
- 18.737, Algebraic groups, Spring 2019.
- 18.705, Commutative algebra, Fall 2019.
- 18.701, Algebra, Fall 2020.
- 18.737, Algebraic groups, Spring 2021.
- 18.02, Multivariable calculus, Fall 2021.
- 18.117, Hodge theory, Spring 2022.
- 18.785, Number theory I, Fall 2022.
- 18.090, Introduction to mathematical reasoning, Spring 2023.
- 18.785, Number theory I, Fall 2023.
- 18.099, Preliminary Arizona Winter School independent study, Fall 2023 (with Aaron Landesman).
From 1998 to 2008, I also presented lectures
to gifted high school students at the
Berkeley Math Circle.
Conferences I have helped organize
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Lehmer conference (co-organized with J. Brillhart, H. Lenstra, and H. Williams), August 24-26, 2000 at U. C. Berkeley.
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Algorithmic number theory
(co-organized with J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, and N. Yui), a semester-long program, Fall 2000, at
MSRI.
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CMI Introductory Workshop in Algorithmic Number Theory
(co-organized with D. Bailey, J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, W. Velez, and N. Yui),
August 14-23, 2000, at
MSRI.
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Arithmetic geometry (chair of organizing committee consisting of N. Elkies, W. McCallum, J.-F. Mestre, and R. Schoof),
December 11-15, 2000, at
MSRI.
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Journées Arithmétiques XXII (member of the scientific committee),
July 2-6, 2001 in Lille, France.
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Rational and integral points on higher-dimensional varieties (co-organized with Yu. Tschinkel),
December 11-20, 2002 at the
AIM Research Conference Center
in Palo Alto, California.
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Arizona Winter School 2003, on Number Theory and Logic (co-organized with A. Pillay and M. Kim),
March 15-19, 2003 at the
University of Arizona
in Tucson, Arizona.
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Lenstra Treurfeest (co-organized with E. Howe, S. Robinson, and E. Schaefer),
a conference marking Hendrik W. Lenstra, Jr.'s retirement from Berkeley,
March 21-23, 2003 at U. C. Berkeley and MSRI.
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Geometry and arithmetic over finite fields (co-organized with J. Buhler),
a special session at the AMS meeting in San Francisco, May 3-4, 2003.
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Algorithmic Number Theory Symposium (ANTS VI), University of Vermont, June 13-18, 2004 (member of program committee).
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Extensions of Hilbert's Tenth Problem (co-organized with A. Shlapentokh, X. Vidaux, K. Zahidi), at the
AIM Research Conference Center
in Palo Alto, California, March 21-25, 2005.
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An Introduction to Recent Applications of Model Theory, a workshop in the Model Theory and Applications to Algebra and Analysis program at
the Isaac Newton Institute,
March 29 - April 8, 2005.
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Rational and Integral Points on Higher-Dimensional Varieties (co-organized with F. Bogomolov, J.-L. Colliot-Thélène, A. Silverberg, Yu. Tschinkel), a semester-long program at MSRI, January 9 - May 19, 2006.
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MSRI Introductory Workshop on Rational and Integral Points on Higher-Dimensional Varieties (chair of organizing committee consisting of F. Bogomolov, J.-L. Colliot-Thélène, D. R. Heath-Brown, J. Kollár, A. Silverberg, Yu. Tschinkel), January 17-21, 2006.
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Arizona Winter School 2006 (co-organized with F. Rodriguez-Villegas, D. Ulmer), on Computational and Algorithmic Aspects of Algebra and Number Theory,
March 11-15, 2006 at the
University of Arizona
in Tucson, Arizona.
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Special session on arithmetic geometry (co-organized with M. Baker),
at the Joint Mathematics Meetings in New Orleans, January 8, 2007.
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Explicit methods for rational points on curves (co-organized with N. Bruin), held at the Banff International Research Station,
February 4-9, 2007.
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Berkeley Undergraduate Research Conference a.k.a. Minamuc (co-organized with a team of Berkeley undergraduates headed by Steven Sam), at U. C. Berkeley, April 7, 2007.
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Modular forms and arithmetic (co-organized with Frank Calegari, Samit Dasgupta, and Richard Taylor), U. C. Berkeley and MSRI, June 28 to July 2, 2008.
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New methods in Hilbert's 10th problem (co-organized with Yu. Matiyasevich and B. Moroz), at the Hausdorff Research Institute for Mathematics, Bonn, Germany, February 9-13, 2009.
- Rational points on varieties,
an AMS special session at the Joint
Mathematics Meetings in Boston
(co-organized
with Jennifer Balakrishnan, Bianca Viray, and Kirsten Wickelgren),
January 5 and 6, 2012.
- BIRS summer school on contemporary methods for solving diophantine equations,
(co-organized
with Michael Bennett, Nils Bruin, Yann Bugeaud, and Samir Siksek),
Banff, June 10-17, 2012.
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Rational points and algebraic cycles,
a semester-long program at the Centre Interfacultaire Bernoulli
in Lausanne, Switzerland
(co-organized with
Hélène Esnault,
Andrew Kresch, and
Alexei Skorobogatov), July 1 to December 31, 2012.
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Cohomological methods in arithmetic geometry,
a workshop at the Universität Zürich
during the Lausanne program above
(co-organized with
Hélène Esnault,
Andrew Kresch, and
Alexei Skorobogatov), September 10-14, 2012.
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Arithmetic of abelian varieties in families,
a workshop during the Lausanne program above
(co-organized with
Hélène Esnault,
Andrew Kresch,
Philippe Michel, and
Alexei Skorobogatov), November 12-16, 2012.
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Explicit methods in number theory,
an Oberwolfach workshop (co-organized with Karim Belabas and Don B. Zagier),
July 14-20, 2013.
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Connections between logic and arithmetic geometry, special session at MathFest, Portland, Oregon, August 7, 2014.
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Explicit methods in number theory,
an Oberwolfach workshop (co-organized with Karim Belabas and Fernando Rodriguez Villegas),
July 5-11, 2015.
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Rational points, one of the seminars during the last week of
the three-week Summer Institute in Algebraic Geometry,
University of Utah,
July 27-31, 2015.
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Grothendieck memorial afternoon, MIT, December 11, 2015.
- Graduate workshop in algebraic geometry for women and mathematicians of minority genders, Harvard and MIT, February 17-18, 2018.
- Explicit methods in number theory, an Oberwolfach workshop (co-organized with Karim Belabas and Fernando Rodriguez Villegas), July 22-28, 2018.
- Arithmetic geometry, number theory, and computation, MIT, August 20-24, 2018.
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2019, Simons Foundation, January 10-11, 2019 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- Arithmetic of low-dimensional abelian varieties, ICERM, June 3-7, 2019 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- Rational points on irrational varieties, Institut Henri Poincaré, June 24-28, 2019 (co-organized with Alexei Skorobogatov).
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2020, Simons Foundation, January 9-10, 2020 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- Workshop on Arithmetic Geometry, Number Theory, and Computation,
at ICERM online, June 1-5, 2020 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- Explicit methods in number theory, an Oberwolfach workshop (co-organized with Karim Belabas and Fernando Rodriguez Villegas), July 18-24, 2021.
- PCMI 2021 Graduate Summer School in number theory [virtual], July 26-30, 2021 (co-organized with Jennifer Balakrishnan and Akshay Venkatesh). This is a precursor to the in-person 2022 PCMI program "Number theory informed by computation".
- Skorobogatov 60 (co-organized with Timothy Browning, Jean-Louis Colliot-Thélène, and David Harari), Institut Henri Poincaré, November 3-5, 2021.
- Joint International Meeting of the AMS, the SMF, and the EMS, Grenoble, France, July 18-22, 2022 (AMS-EMS-SMF Program Committee chair).
- Number theory informed by computation, PCMI, July 17-August 6, 2022 (co-organized with Jennifer Balakrishnan and Akshay Venkatesh). Includes a research program, graduate summer school, undergraduate summer school, and more.
- Arithmetic geometry informed by computation, an AMS special session at the Joint Mathematics Meetings in Boston, January 4 and 5, 2023 (co-organized with Jennifer Balakrishnan and Andrew Sutherland).
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2023, Simons Foundation, January 11-12, 2023 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2024, Simons Foundation, January 11-12, 2024 (co-organized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
- The Mordell conjecture 100 years later, MIT, July 8-12, 2024 (co-organized with Jennifer Balakrishnan, Philipp Habegger, Andrew V. Sutherland, and Wei Zhang), just before ANTS XVI.
- Explicit methods in number theory, an Oberwolfach workshop (co-organized with Karim Belabas and Fernando Rodriguez Villegas), September 1-7, 2024.
Past editorial positions
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Journal
of the American Mathematical Society,
associate editor, 2000-2003 and 2004-2010.
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Journal
of Number Theory, editorial board member, 2003-2004.
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Journal
de Théorie des Nombres de Bordeaux,
editorial board member, 1999-2006.
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International Mathematics Research Notices, editor, 2006-2008.
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LMS Journal of Computation and Mathematics, editorial board member, 2007-2011.
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A K Peters Research Notes in Mathematics book series, editorial board member, 2005-2014.
Past professional activities
- Bowen Lectures Committee (U. C. Berkeley mathematics department), 2002-2004.
- Committee on Prizes (U. C. Berkeley), member 2000-2006, chair 2003-2006.
- Preliminary Exam Committee (U. C. Berkeley mathematics department), chair, 2000-2006.
- Calculus and Course Committee (U. C. Berkeley mathematics department), chair, 2006-2007.
- Mathematical Reviews, reviewer, 2006-2007.
- Committee on Computing and Communications (U. C. Berkeley), 2006-2008.
- Vice Chair for Undergraduate Affairs (U. C. Berkeley mathematics department), 2006-2008.
- MAA Committee on the Putnam Prize Competition, 2008, 2009, 2010.
- MIT Task Force on Improving Graduate Admissions Processes, 2011.
- MIT Committee on Graduate Admissions, 2012-2013.
- MIT Mathematics Department Graduate Co-Chair (with Peter Shor and Gigliola Staffilani), 2009-2012.
- MIT Mathematics Department Committee on Graduate Admissions, 2008-2015.
- MIT Mathematics Department Executive Committee, 2009-2015.
- AMS Centennial Fellowship Committee, 2015-2017.
- AMS-MSRI Math Circle Library Advisory Board, 2007-2016.
- MIT Freshman Advisor, 2013-2015 and 2016-2017.
- AMS Committee to Select the Winner of the E. H. Moore Research Article Prize, 2012-2018 (chair 2014-2016).
- AMS Nominating Committee, 2017-2019.
- MIT Mathematics Council, 2013-2015, 2016-17, 2018-19.
- MIT Department of Athletics, Physical Education, and Recreation Advisory Board, 2017-2020.