Any comments about how to improve any of these notes are welcome.


Notes/Slides for talks I have given.

These are the slides or notes that I wrote up for talks that I have given.

  1. Sieving, Property Tau, and 3-Manifolds University of Wisconsin-Madison,
    Group Theory Seminar. PDF.

  2. Eulerian Series as Modular Forms University of Illinois Urbana-Champagne and University of Wisconsin Madison,
    Number Theory Seminar. PDF.

  3. Entropy of Convolutions on the Circle UCLA Summer School in Ergodic Theory,
    September 17-22, 2006.PDF.

  4. Riemann Surfaces. University of Wisconsin Algebraic Topology Class,
    April 21, 2006.PDF.

  5. Points On Curves. University of Wisconsin Undergraduate Math Club,
    February 13, 2006.PDF.

  6. p-adic and Combinatorial Properties of Modular Form Coefficients. University of Wisconsin Number Theory Seminar,
    November 22, 2005. PDF.

  7. All The Tricks I Know. Bucknell University Student Putnam Session,
    September 29, 2005.PDF.

  8. Reducing Complicated Objects to Simple Ones: Coefficients of Modular Forms. Bucknell University Student Colloquium Series,
    September 27, 2005. PDF.


Class Notes.

These are the written notes for classes I have taken. I take full responsibility for any mistakes that may appear in the notes.

  1. Elliptic Curves and Modular Forms taught by Jordan Ellenberg
    Spring 2008, University of Wisconsin. PDF.

  2. Introduction to the Langlands Program taught by Yannan Qiu
    Spring 2008, University of Wisconsin. PDF.

  3. Rational Points on Varieties taught by Jordan Ellenberg
    Fall 2005, University of Wisconsin. PDF.

  4. Elliptic Curves and Modular Forms taught by Nigel Boston
    Spring 2006, University of Wisconsin. PDF. Errata from Robert Ash PDF

  5. Solutions to Problems from
    Stein and Shakarchi's Complex Analysis Book
    PDF.


Notes For Talks I have attended.

These are notes from various talks that I have attended. I take full responsibility for all mistakes or incorrect statements that appear in the notes.

  1. Matthew Young: Restricted $L^2$ Norm of a $GL_3$ Maass Form
    November 12, 2010, Stanford University Number Theory Seminar. PDF.

  2. Jeff Hoffstein: Shifted Multiple Dirichlet Series
    November 5, 2010, Stanford University Number Theory Seminar. PDF.

  3. Akshay Venkatesh: Spherical Varieties
    October 29, 2010, Stanford University Quantum Groups Seminar. PDF.

  4. Takashi Taniguchi: The Secondary Term in the Counting Function of Cubic Field Discriminants
    October 29, 2010, Stanford University Number Theory Seminar. PDF.

  5. George Andrews: Orthogonal Polynomials
    March 8, 2010, workshop on Mock Modular Forms and q-series at American Institute of Mathematics. PDF.

  6. Andrew Snowden: Elements of Automorphic Theory in Lifting Theorems
    January 29, 2010, Stanford University Modularity Lifting Seminar. PDF.

  7. Brian Conrey: Zeros of L-functions
    January 29, 2010, Stanford University Informal Number Theory Seminar. PDF.

  8. Peter Stevenhagen: Inverse Point Counting
    January 29, 2010, Stanford University Number Theory Seminar. PDF.

  9. George Andrews: Partitions, Orthogonal Polynomials, and q-series
    January 14, 2010, Joint Meeting of the AMS and MAA in San Francisco. PDF.

  10. Joe Harris: On The Interpolation Problem
    January 13, 2010, Joint Meeting of the AMS and MAA in San Francisco. PDF.

  11. Manjul Bhargava: The Factorial Function, Integer Valued Polynomials, and p-adic Calculus
    January 13, 2010, Joint Meeting of the AMS and MAA in San Francisco. PDF.

  12. Notes from the Problem Session on May 22 during the conference on Analytic Number Theory and Higher Rank Groups
    May 22, 2008, New York University. PDF.

  13. Philippe Michel: Three introductory talks on the distribution of CM points, subconvexity, and generalizations and a research talk on uniform subconvexity for L-functions on GL(2).
    May 19 - 22, 2008, Analytic Number Theory and Higher Rank Groups. PDF.

  14. Akshay Venkatesh: Analytic Number Theory in Function Fields
    April 10, 2008, University of Toronto Colloquium. PDF.

  15. Akshay Venkatesh: Random Permutations in Number Theory
    April 9, 2008, Clay-Fields Conference on Additive Combinatorics, Number Theory, and Harmonic Analysis. PDF.

  16. Terrence Tao: Mobius and Nilsequence Conjecture
    April 6, 2008, Clay-Fields Conference on Additive Combinatorics, Number Theory, and Harmonic Analysis. Two talks PDF.

  17. Antal Balog: Trigonometric Sums with Multiplicative Coefficients
    April 6, 2008, Clay-Fields Conference on Additive Combinatorics, Number Theory, and Harmonic Analysis. PDF.

  18. Jordan Ellenberg: Congruence Subgroups and Cohomology
    February 18, 2008, University of Wisconsin Group Theory seminar. PDF.

  19. Jeremy Rouse: The Birch and Swinnerton-Dyer Conjecture.
    August 15, 2005, University of Wisconsin Summer REU in Mathematics. PDF.

  20. Ben Brubaker: Multiple Dirichlet Series.
    Sepetemer 22, 2005, University of Wisconsin Number Theory Seminar. PDF.

  21. Andrew Booker.
    November 4, 2005, 2005, Midwest Number Theory Conference held at University of Wisconsin. PDF.

  22. Craig Westerland: An Introduction to Stable Homotopy Theory.
    November 22, 2005, University of Wisconsin Algebraic Topology Class. PDF.

  23. Jordan Ellenberg: An Application of Ergodic Theory to a Classical Problem in Number Theory
    December 9, 2005, University of Wisconsin Colloquium. PDF.


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