CMI-IMSc Number Theory Seminar
Date: Tuesday, 8 April 2025
Time: 3:30 to 4:30 pm
Venue: Seminar Hall, CMI
Second order terms in arithmetic statistics
Arul Shankar
University of Toronto.
08-04-25

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Abstract

In arithmetic statistics, we have well developed heuristics for the distributions of discriminants of number fields (due to Malle and Bhargava), distributions of class groups of number fields (due to Cohen--Lenstra and Cohen--Lenstra--Martinet), and distributions of ranks (due to Goldfeld and Katz--Sarnak) and Selmer groups (due to Poonen--Rains) of elliptic curves. However, secondary terms in these distributions are far more mysterious and remain unknown (even conjecturally). In this talk, I will discuss this set of questions, and talk about recent joint work with Jacob Tsimerman, in which we determine secondary terms for the counts in some families of quartic fields.