Bay Area Algebraic Number Theory and Arithmetic Geometry Day III
Saturday, October 22, 2011
University of California, Santa Cruz
Room: McHenry Library, room 1240
Matthew Baker, University of California, Berkeley
Pierre Colmez, Institut de Mathématiques de Jussieu
Cameron Franc, University of California, Santa Cruz
Dinakar Ramakrishnan, California Institute of Technology
William Stein, University of Washington
All talks will be in room 1240 on the first floor of McHenry. Coffee breaks will be in room 1257.
|Dinner, "I Love Sushi"
Please RSVP to sdasgup2 (at) ucsc (dot) edu
Titles and Abstracts:
Matt Baker, "The Poincare-Lelong formula for non-Archimedean analytic curves and applications to tropical geometry"
I will discuss how one can formulate and prove a non-Archimedean Berkovich space analogue of the classical formula ddc(log|f|)=δdiv(f) for a nonzero rational function f on a compact Riemann surface X. I will then explain various applications of this formula to tropical geometry, including the "specialization lemma", tropical implicitization, and the "tropical j-invariant".
Pierre Colmez, "On the p-adic local Langlands correspondence for GL2(Qp)"
Cameron Franc, "CM values of Shimura-Maass derivatives of rigid analytic modular forms"
In this talk we will begin by recalling Shimura's result on the algebraicity of CM values of certain nonholomorphic (Shimura-Maass) derivatives of modular forms. We will then introduce the p-adic upper half plane and rigid analytic modular forms. Finally we will introduce an analogue of the Shimura-Maass operator for rigid analytic modular forms, and state a p-adic version of Shimura's classical theorem.
Dinakar Ramakrishnan, "Galois symbols on the square of an elliptic curve"
In the this talk we will discuss some results, proved in joint works with Murre, on the Galois symbols modulo an odd prime p, on the Albanese kernel of E x E, E an elliptic curve over a number field F or a local completion. These symbols take values in the second Galois cohomology group H2(F, sym2(E[p])), and are induced by taking cup products of classes in H1(F, E[p]) defined by a pair of points P, Q in E(F). We show that for large enough p, such symbols are trivial, providing partial evidence for a conjecture of Bloch and Beilinson. We will start from scratch and explain the problem and the method.
William Stein, "Numerical Computation of Chow-Heegner Points"
Chow-Heegner points, as are being actively pursed by
Darmon, Rotger, et al., are quite general. In this talk, we consider
a special case that has a simple concrete description due to Shouwu
Zhang. Given a pair E, F of elliptic curves, and a fixed choice of
maps X0(N)-->E and X0(N)-->F, we associate a rational point P on E.
In this talk we will describe a rarely elementary numerical approach
to computing P, state some motivating results of Zhang et al. about
the height of P, and present a new table of data.
The closest parking is at the Hahn parking lot. Parking is free and no permit is required on Saturdays, as long as you park in a legal parking space and do not block emergency access, or park in spaces that are posted and reserved for special use.
There is a foot bridge that connects the Hahn parking lot to McHenry Library.
If you click on this map and zoom out one level, the bridge is indicated by a
dotted line. Halfway through the bridge, there is a path that leads to the left, but you want to ignore this path and continue straight until the
end of the bridge. After crossing the bridge, make a sharp left slightly downhill to enter the building at the
first level. (The main entrance is actually on the second level, so if you enter here you will have to take
the elevator down one level.)
There is no formal registration, but if you plan to attend, we would appreciate an email to sdasgup2 at ucsc dot edu to
help plan the event, especially if you plan to attend the dinner afterwards.
There will be a dinner following the conference, at 6pm at "I Love Sushi", 516 Front St,
in downtown Santa Cruz.