Embedded Files
Welcome
Welcome
Welcome to the Emory ARithmetic Statistics Student Seminar (EARSSS)! This site will serve as the homepage, with scheduling information and resources.
Organizers: Santiago Arango-Piñeros, Christopher Keyes, and David Zureick-Brown.
This seminar will be held in Fall 2020 online on Mondays from 11:00 am - 12:30 pm (Atlanta time). This block will be broken into two parts, with a 10 minute break, so we'll have about 80 minutes of talks each week. Please email an organizer to joint the meeting list, where we will send out the Zoom links.
The goal of this learning seminar is to cover a broad range of topics of current interest in arithmetic statistics. The Fall 2020 semester will focus more on subjects related to number fields and heuristics of class groups, while the Spring 2021 semester will incorporate more geometric themes.
Resources
Resources
Below is a running list of papers related to the seminar's goals. Those that we reference most during the talks are indicated on the schedule.
[ASVW] Altug-Shankar-Varma-Wilson, The number of quartic D_4 fields ordered by conductor.
[Bha1] Bhargava, Higher composition laws and applications, ICM 2006.
[Bha2] Bhargava, On the classification of rings of small rank, 2009 AWS notes.
[Bha3] Bhargava, Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants.
[BGW] Bhargava-Gross-Wang, A positive proportion of locally soluble hyperelliptic curves over Q have no point over any odd degree extension.
[BST] Bhargava-Shankar-Tsimerman, On Davenport-Heilbronn theorems and second order terms.
[Coh] Cohen, Constructing and counting number fields, survey.
[CM] Cohen-Martinet, Class groups of number fields: numerical heuristics.
[CL] Cohen-Lenstra, Heuristics on class groups of number fields.
[DH] Davenport-Heilbronn, On the density of discriminants of cubic fields II.
[Ell] Ellenberg, Geometric analytic number theory, 2014 AWS notes
[EV] Ellenberg-Venkatesh, The number of extensions of a number field with fixed degree and bounded discriminant.
[FW] Friedman-Washington, On the distribution of divisor class groups of curves over a finite field.
[HS] Ho-Shankar, Miscellaneous problems in arithmetic geometry, 2014 AWS Problems.
[Lan] Landesman, Notes on counting extensions of degrees 2 and 3, following Bhargava, Notes.
[Len] Lenstra, The Chebotarev Density Theorem.
[LS] Lenstra-Stevenhagen, Chebotarev and his density theorem.
[LWZB] Liu--Wood--Zurieck-Brown, A predicted distribution for Galois groups of maximal unramified extensions.
[Poo] Poonen, A brief summary of the statements of class field theory.
[PS1] Poonen-Stoll, The Cassels-Tate pairing on polarized abelian varieties.
[PS2] Poonen-Stoll, A local-global principle for densities.
[PS3] Poonen-Stoll, Most odd degree hyperelliptic curves have only one rational point.
[Mal] Malle, On the distribution of class groups in number fields.
[Mil] J.S. Milne, Algebraic Number Theory.
[Sch] Schmidt, Number fields of given degree and bounded discriminant.
[Ser] Serre, Lectures on N_p(X).
[Woo] Wood, Asymptotics for Number Fields and Class Groups, 2014 AWS notes.
Page updated
Google Sites
Report abuse