Courses

Princeton University

Math 102, Calculus, Spring 1996 and Spring 1997.

University of California, Berkeley

Math 185, Complex analysis, Fall 1997.

Math H1B, Honors calculus, Fall 1998.

Math 256B, Algebraic geometry, Spring 1999.

Math 254B, Number theory, Spring 2000.
 Math 54, Linear algebra and differential equations, Spring 2001.
 Math 55, Discrete mathematics, Fall 2001.

Math 274, Rational points on varieties, Spring 2003.

Math 250A, Groups, rings, and fields, Fall 2003.

Math 140, Metric differential geometry, Spring 2004.

Math 185, Complex analysis, Spring 2004.

Math 160, History of mathematics, Spring 2005.

Math 16A, Analytic geometry and calculus, Fall 2006.

Institut Henri Poincaré

Rational points on curves, during the "Explicit methods in number theory" trimester, Fall 2004.

padic approaches to rational points on curves, during the "Reinventing rational points" trimester, AprilJuly 2019.

MIT

18.821, Project laboratory in mathematics, Fall 2007,
with Susan Ruff and David Vogan.

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 918, 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

Lehmer conference (coorganized with J. Brillhart, H. Lenstra, and H. Williams), August 2426, 2000 at U. C. Berkeley.

Algorithmic number theory
(coorganized with J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, and N. Yui), a semesterlong program, Fall 2000, at
MSRI.

CMI Introductory Workshop in Algorithmic Number Theory
(coorganized with D. Bailey, J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, W. Velez, and N. Yui),
August 1423, 2000, at
MSRI.

Arithmetic geometry (chair of organizing committee consisting of N. Elkies, W. McCallum, J.F. Mestre, and R. Schoof),
December 1115, 2000, at
MSRI.

Journées Arithmétiques XXII (member of the scientific committee),
July 26, 2001 in Lille, France.

Rational and integral points on higherdimensional varieties (coorganized with Yu. Tschinkel),
December 1120, 2002 at the
AIM Research Conference Center
in Palo Alto, California.

Arizona Winter School 2003, on Number Theory and Logic (coorganized with A. Pillay and M. Kim),
March 1519, 2003 at the
University of Arizona
in Tucson, Arizona.

Lenstra Treurfeest (coorganized with E. Howe, S. Robinson, and E. Schaefer),
a conference marking Hendrik W. Lenstra, Jr.'s retirement from Berkeley,
March 2123, 2003 at U. C. Berkeley and MSRI.

Geometry and arithmetic over finite fields (coorganized with J. Buhler),
a special session at the AMS meeting in San Francisco, May 34, 2003.

Algorithmic Number Theory Symposium (ANTS VI), University of Vermont, June 1318, 2004 (member of program committee).

Extensions of Hilbert's Tenth Problem (coorganized with A. Shlapentokh, X. Vidaux, K. Zahidi), at the
AIM Research Conference Center
in Palo Alto, California, March 2125, 2005.

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.

Rational and Integral Points on HigherDimensional Varieties (coorganized with F. Bogomolov, J.L. ColliotThélène, A. Silverberg, Yu. Tschinkel), a semesterlong program at MSRI, January 9  May 19, 2006.

MSRI Introductory Workshop on Rational and Integral Points on HigherDimensional Varieties (chair of organizing committee consisting of F. Bogomolov, J.L. ColliotThélène, D. R. HeathBrown, J. Kollár, A. Silverberg, Yu. Tschinkel), January 1721, 2006.

Arizona Winter School 2006 (coorganized with F. RodriguezVillegas, D. Ulmer), on Computational and Algorithmic Aspects of Algebra and Number Theory,
March 1115, 2006 at the
University of Arizona
in Tucson, Arizona.

Special session on arithmetic geometry (coorganized with M. Baker),
at the Joint Mathematics Meetings in New Orleans, January 8, 2007.

Explicit methods for rational points on curves (coorganized with N. Bruin), held at the Banff International Research Station,
February 49, 2007.

Berkeley Undergraduate Research Conference a.k.a. Minamuc (coorganized with a team of Berkeley undergraduates headed by Steven Sam), at U. C. Berkeley, April 7, 2007.

Modular forms and arithmetic (coorganized with Frank Calegari, Samit Dasgupta, and Richard Taylor), U. C. Berkeley and MSRI, June 28 to July 2, 2008.

New methods in Hilbert's 10th problem (coorganized with Yu. Matiyasevich and B. Moroz), at the Hausdorff Research Institute for Mathematics, Bonn, Germany, February 913, 2009.
 Rational points on varieties,
an AMS special session at the Joint
Mathematics Meetings in Boston
(coorganized
with Jennifer Balakrishnan, Bianca Viray, and Kirsten Wickelgren),
January 5 and 6, 2012.
 BIRS summer school on contemporary methods for solving diophantine equations,
(coorganized
with Michael Bennett, Nils Bruin, Yann Bugeaud, and Samir Siksek),
Banff, June 1017, 2012.

Rational points and algebraic cycles,
a semesterlong program at the Centre Interfacultaire Bernoulli
in Lausanne, Switzerland
(coorganized with
Hélène Esnault,
Andrew Kresch, and
Alexei Skorobogatov), July 1 to December 31, 2012.

Cohomological methods in arithmetic geometry,
a workshop at the Universität Zürich
during the Lausanne program above
(coorganized with
Hélène Esnault,
Andrew Kresch, and
Alexei Skorobogatov), September 1014, 2012.

Arithmetic of abelian varieties in families,
a workshop during the Lausanne program above
(coorganized with
Hélène Esnault,
Andrew Kresch,
Philippe Michel, and
Alexei Skorobogatov), November 1216, 2012.

Explicit methods in number theory,
an Oberwolfach workshop (coorganized with Karim Belabas and Don B. Zagier),
July 1420, 2013.

Connections between logic and arithmetic geometry, special session at MathFest, Portland, Oregon, August 7, 2014.

Explicit methods in number theory,
an Oberwolfach workshop (coorganized with Karim Belabas and Fernando Rodriguez Villegas),
July 511, 2015.

Rational points, one of the seminars during the last week of
the threeweek Summer Institute in Algebraic Geometry,
University of Utah,
July 2731, 2015.

Grothendieck memorial afternoon, MIT, December 11, 2015.
 Graduate workshop in algebraic geometry for women and mathematicians of minority genders, Harvard and MIT, February 1718, 2018.
 Explicit methods in number theory, an Oberwolfach workshop (coorganized with Karim Belabas and Fernando Rodriguez Villegas), July 2228, 2018.
 Arithmetic geometry, number theory, and computation, MIT, August 2024, 2018.
 Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2019, Simons Foundation, January 1011, 2019 (coorganized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
 Arithmetic of lowdimensional abelian varieties, ICERM, June 37, 2019 (coorganized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
 Rational points on irrational varieties, Institut Henri Poincaré, June 2428, 2019 (coorganized with Alexei Skorobogatov).
 Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2020, Simons Foundation, January 910, 2020 (coorganized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
 Workshop on Arithmetic Geometry, Number Theory, and Computation,
at ICERM online, June 15, 2020 (coorganized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
 Explicit methods in number theory, an Oberwolfach workshop (coorganized with Karim Belabas and Fernando Rodriguez Villegas), July 1824, 2021.
 PCMI 2021 Graduate Summer School in number theory [virtual], July 2630, 2021 (coorganized with Jennifer Balakrishnan and Akshay Venkatesh). This is a precursor to the inperson 2022 PCMI program "Number theory informed by computation".
 Skorobogatov 60 (coorganized with Timothy Browning, JeanLouis ColliotThélène, and David Harari), Institut Henri Poincaré, November 35, 2021.
 Joint International Meeting of the AMS, the SMF, and the EMS, Grenoble, France, July 1822, 2022 (AMSEMSSMF Program Committee chair).
 Number theory informed by computation, PCMI, July 17August 6, 2022 (coorganized 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 (coorganized with Jennifer Balakrishnan and Andrew Sutherland).
 Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting 2023, Simons Foundation, January 1112, 2023 (coorganized 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 1112, 2024 (coorganized with Jennifer Balakrishnan, Noam Elkies, Brendan Hassett, Andrew Sutherland, and John Voight).
 The Mordell conjecture 100 years later, MIT, July 812, 2024 (coorganized with Jennifer Balakrishnan, Philipp Habegger, Andrew V. Sutherland, and Wei Zhang), just before ANTS XVI.
 Explicit methods in number theory, an Oberwolfach workshop (coorganized with Karim Belabas and Fernando Rodriguez Villegas), September 17, 2024.
Past editorial positions

Journal
of the American Mathematical Society,
associate editor, 20002003 and 20042010.

Journal
of Number Theory, editorial board member, 20032004.

Journal
de Théorie des Nombres de Bordeaux,
editorial board member, 19992006.

International Mathematics Research Notices, editor, 20062008.

LMS Journal of Computation and Mathematics, editorial board member, 20072011.

A K Peters Research Notes in Mathematics book series, editorial board member, 20052014.
Past professional activities
 Bowen Lectures Committee (U. C. Berkeley mathematics department), 20022004.
 Committee on Prizes (U. C. Berkeley), member 20002006, chair 20032006.
 Preliminary Exam Committee (U. C. Berkeley mathematics department), chair, 20002006.
 Calculus and Course Committee (U. C. Berkeley mathematics department), chair, 20062007.
 Mathematical Reviews, reviewer, 20062007.
 Committee on Computing and Communications (U. C. Berkeley), 20062008.
 Vice Chair for Undergraduate Affairs (U. C. Berkeley mathematics department), 20062008.
 MAA Committee on the Putnam Prize Competition, 2008, 2009, 2010.
 MIT Task Force on Improving Graduate Admissions Processes, 2011.
 MIT Committee on Graduate Admissions, 20122013.
 MIT Mathematics Department Graduate CoChair (with Peter Shor and Gigliola Staffilani), 20092012.
 MIT Mathematics Department Committee on Graduate Admissions, 20082015.
 MIT Mathematics Department Executive Committee, 20092015.
 AMS Centennial Fellowship Committee, 20152017.
 AMSMSRI Math Circle Library Advisory Board, 20072016.
 MIT Freshman Advisor, 20132015 and 20162017.
 AMS Committee to Select the Winner of the E. H. Moore Research Article Prize, 20122018 (chair 20142016).
 AMS Nominating Committee, 20172019.
 MIT Mathematics Council, 20132015, 201617, 201819.
 MIT Department of Athletics, Physical Education, and Recreation Advisory Board, 20172020.