NTS Spring 2013/Abstracts

January 24

Tamar Ziegler (Technion)

Title: An inverse theorem for the Gowers norms

Abstract: Gowers norms play an important role in solving linear equations in subsets of integers - they capture random behavior with respect to the number of solutions. It was conjectured that the obstruction to this type of random behavior is associated in a natural way to flows on nilmanifolds. In recent work with Green and Tao we settle this conjecture. This was the last piece missing in the Green-Tao program for counting the asymptotic number of solutions to rather general systems of linear equations in primes.

January 31

William Stein (U. of Washington)

Title: How explicit is the explicit formula?

Abstract: Consider an elliptic curve E. The explicit formula for E relates a sum involving the numbers ap(E) to a sum of three quantities, one involving the analytic rank of the curve, another involving the zeros of the L-series of the curve, and the third, a bounded error term. Barry Mazur and I are attempting to see how numerically explicit – for particular examples – we can make each term in this formula. I'll explain this adventure in a bit more detail, show some plots, and explain what they represent. (This is joint work with Barry Mazur).

February 7

Nigel Boston (Madison)

Title: A refined conjecture on factoring iterates of polynomials over finite fields

Abstract: tba

Organizer contact information

Robert Harron

Zev Klagsbrun

Sean Rostami

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