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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.
• 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.

From 1998 to 2008, I also presented lectures to gifted high school students at the Berkeley Math Circle.

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Conferences I have helped organize

• Lehmer conference (co-organized with J. Brillhart, H. Lenstra, and H. Williams), August 24-26, 2000 at U. C. Berkeley.
• Algorithmic number theory semester (co-organized with J. Buhler, C. Dwork, H. Lenstra, A. Odlyzko, and N. Yui), Fall 2000, at MSRI.
• 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.
• Arithmetic geometry (chair of organizing committee consisting of N. Elkies, W. McCallum, J.-F. Mestre, and R. Schoof), December 11-15, 2000, at MSRI.
• Journées Arithmétiques XXII (member of the scientific committee), July 2-6, 2001 in Lille, France.
• 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.
• 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.
• 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.
• 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.
• Algorithmic Number Theory Symposium (ANTS VI), University of Vermont, June 13-18, 2004 (member of program committee).
• 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.
• 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 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.
• 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.
• 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.
• Special session on arithmetic geometry (co-organized with M. Baker), at the Joint Mathematics Meetings in New Orleans, January 8, 2007.
• Explicit methods for rational points on curves (co-organized with N. Bruin), held at the Banff International Research Station, February 4-9, 2007.
• 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.
• 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.
• 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.

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Past editorial positions

• Journal of the American Mathematical Society, associate editor, 2000-2003 and 2004-2010.
• Journal of Number Theory, editorial board member, 2003-2004.
• Journal de Théorie des Nombres de Bordeaux, editorial board member, 1999-2006.
• International Mathematics Research Notices, editor, 2006-2008.
• LMS Journal of Computation and Mathematics, editorial board member, 2007-2011.

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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.