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Student supervision






    BSc theses

  • 2005, Matthew E. Lane, Princeton University

    I was the supervisor for M. Lane's BSc thesis Elliptic curve analogues of the twin prime conjecture. Matt is currently a PhD student in mathematics at UCLA.

    The thesis was awarded the first prize in the mathematics-physics section and the third prize in the all-discipline section at the Undergraduate Research Symposium organized at Princeton University in May 2005.

  • 2004, Jeffrey H. Law, Princeton University

    I was co-supervisor (with Elias Stein) for J. Law's BSc thesis The Hardy-Littlewood method.



    Student projects

    The following are student projects written under my supervision.

  • Graduate projects

    • 2007, Raymond Fuller, Charles Moss and Drew Shulman, The normal order of the prime divisors of p-1, UIC

    • 2007, Holly Krieger, Travis Taylor and Matt Wechter, Mertens' theorem and the Riemann zeta function, UIC

    • 2007, Jonnathan Schneider, Randall Stading and Andrew Sward, The Barban-Davenport-Halberstam theorem, UIC

    • 2007, Kin Hang Chan, David Ilyaguyev and Katherine Perusek, On the Titchmarsh divisor problem, UIC

    • 2007, Richard Abdelkerim, Chris Sabino and Kanth Sishtla, The Hilbert symbol and the Turan sieve, UIC

    • 2004, Seshadhri Comandur, Twin primes, Princeton University

    • 2004, Nitin Saxena, Euclidean proofs for primes in an arithmetic progression, Princeton University


  • Junior projects

    • 2005, Allison Bishop, Computing the order of the group of points on an elliptic curve over F_p, Princeton University

    • 2005, Josh Brodie, Public key cryptosystems, discrete logarithms and elliptic curves, Princeton University

    • 2005, Rohan Kapadia, Factoring with elliptic curves, Princeton University

    • 2005, Paul Nelson, Supersingular primes for elliptic curves over Q, Princeton University

    • 2004, Gabriel R. Doyle, An introduction to the ABC conjecture, Princeton University

    • 2004, Leo Goldmakher, An application of sieve methods to probabilistic Galois theory, Princeton University

    • 2004, Matthew E. Lane, Exploring the ABC conjecture, Princeton University

    • 2004, Jeffrey H. Law, The Schnirelman density on Waring's problem, Princeton University

    • 2004, Paul Nelson, Schnirelman's density theorem and Waring's problem for polynomials, Princeton University

    • 2004, Anna Pierrehumbert, An introduction to rational points on elliptic curves, Princeton University

    • 2004, Alexey Spiridonov, The Schnirelman-Linnik approach to Waring's problem, Princeton University



    Prospective students

  • To come: information for students interested in working under my supervision






Last modified: Fall 2007