Difference between revisions of "NTS Spring 2013/Abstracts"
(→January 24) |
(add title and abstract for Kai-Wen's talk) |
||
Line 48: | Line 48: | ||
<br> | <br> | ||
− | + | ||
− | == | + | == March 7 == |
<center> | <center> | ||
{| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspacing="20" | ||
|- | |- | ||
− | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | ''' | + | | bgcolor="#F0A0A0" align="center" style="font-size:125%" | '''Kai-Wen Lan''' (Minnesota) |
|- | |- | ||
− | | bgcolor="#BCD2EE" align="center" | Title: | + | | bgcolor="#BCD2EE" align="center" | Title: Galois representations for regular algebraic cuspidal automorphic representations over CM fields |
|- | |- | ||
| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | | ||
− | Abstract: | + | Abstract: After reviewing what the title means (!) and providing some preliminary explanations, I will report on my joint work with Michael Harris, Richard Taylor, and Jack Thorne on the construction of ''p''-adic Galois representations for regular algebraic cuspidal automorphic representations over CM (or totally real) fields, without hypothesis on self-duality or ramification. The main novelty of this work is the removal of the self-duality hypothesis; without this hypothesis, we cannot realize the desired Galois representation in the ''p''-adic étale cohomology of any of the varieties we know. I will try to explain our main new idea without digressing into details in the various blackboxes we need. I will supply conceptual (rather than technical) motivations for everything we introduce. |
− | representations | ||
− | fields | ||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
|} | |} | ||
</center> | </center> | ||
<br> | <br> | ||
− | + | <!-- | |
== October 11 == | == October 11 == | ||
Revision as of 17:01, 24 January 2013
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 a_{p}(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 |
March 7
Kai-Wen Lan (Minnesota) |
Title: Galois representations for regular algebraic cuspidal automorphic representations over CM fields |
Abstract: After reviewing what the title means (!) and providing some preliminary explanations, I will report on my joint work with Michael Harris, Richard Taylor, and Jack Thorne on the construction of p-adic Galois representations for regular algebraic cuspidal automorphic representations over CM (or totally real) fields, without hypothesis on self-duality or ramification. The main novelty of this work is the removal of the self-duality hypothesis; without this hypothesis, we cannot realize the desired Galois representation in the p-adic étale cohomology of any of the varieties we know. I will try to explain our main new idea without digressing into details in the various blackboxes we need. I will supply conceptual (rather than technical) motivations for everything we introduce. |
Organizer contact information
Sean Rostami
Return to the Number Theory Seminar Page
Return to the Algebra Group Page