NTS Spring 2013/Abstracts
January 24
| Tamar Ziegler (Technion) |
| Title: An inverse theorem for the Gowers norms |
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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? |
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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 |
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Abstract: tba |
Organizer contact information
Sean Rostami
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