Diff for "MSRItemp/PostdocSeminar"

The Arithmetics Statistic postdoc seminar, organized by Jonathan Bober and Kaneenika Sinha, meets Mondays from 10 to 10:50 a.m. The Free Boundary Problems postdoc seminar meets immediately afterwards, and then MSRI will have pizza for us at 12.

Note to speakers/attendees

MSRI expects that all postdocs, in both programs, should attend both postdoc seminars, and so speakers may wish to keep in mind the fact that a significant portion of the audience may not be number theorists. On the other hand, it is likely that most of the audience will be in the Arithmetic Statistics program, and perhaps the primary purpose of this seminar should for participants in the Arithmetic Statistics program to tell other participants in the Arithmetic Statistics program something about what they are interested in and why they are interested in it.

Also, we take the name "Postdoc Seminar" to mean that the speakers are postdocs, not that the audience members must be composed of postdocs, and everyone is welcome to attend.

Current anticipated schedule

Abstracts

• February 7th, Andrew Yang: "Low-Lying zeros of Dedekind zeta functions"
• Abstract: The Katz-Sarnak philosophy asserts that to any "naturally defined family" of L-functions, there should be an associated symmetry group which determines the distribution of the low-lying zeros (as well as other statistics) of those L-functions. We consider the family of Dedekind zeta functions of cubic number fields, and we predict that the associated symmetry group is symplectic. There are three main ingredients: the explicit formula, work of Davenport-Heilbronn on counting cubic fields and the proportion of fields in which rational primes have given splitting type, and power-saving error terms for these counts, first obtained by Belabas-Bhargava-Pomerance.

• February 14th, Gonzalo Tornaría: The Brandt module of ternary quadratic forms

• Abstract: As proposed by Birch, one can construct partial Brandt matrices by the method of neighboring lattices for ternary quadratic forms.
• In this talk we will present a refinement of the classical notion of proper equivalence of lattices which leads to the construction of the full Brandt matrices, at least in the squarefree level case. Moreover this refinement leads naturally (and is motivated by!) to the definition of generalized ternary theta series.
• We apply these ideas to the construction of modular forms of half integral weight, giving an explicit version of the Shimura correspondence which generalizes results of Eichler, Gross, Ponomarev, Birch, Schulze-Pillot, and Lehman.