MATH 649 : Arithmetic statistics and Bhargavology
Lecturer: Rob Harron
Fall 2017
Lectures: TTh 1:30pm–2:45pm
Keller 403

Recommended textbook: There are no textbooks on the subject!
Office Hours: tbd
Course material:
Lecture 1Introduction, motivation, and sieving for squarefree numbers
Lecture 2Counting quadratic fields, interlude on Dirichlet series and Tauberian theorems
(Source: Appendix of Ellenberg–Pierce–Wood)
Lecture 3Malle's conjecture: precise statement and examples
(Source: Malle's On the distribution of Galois groups, II)
Assignment 1
(latex file)
Lecture 4Malle's heuristic reasoning, the Wirsing–Odoni method
(Source: Malle loc. cit., Finch–Martin–Sebah, Prop. 4)
Lecture 5Analytic part of counting cyclic cubics, some class field theory
Lecture 6Conductors and discriminants, algebraic part of counting cyclic cubics
Lecture 7Counting V4-quartics, part I
Lecture 8Counting V4-quartics, part II
Lecture 9Rings of rank n, parametrizing quadratic algebras over a PID, part I
(Source: O'Dorney's Rings of small rank over a Dedekind domain and their ideals)
Lecture 10Parametrizing quadratic algebras over a PID, part II
Lecture 11Parametrizing quadratic algebras over a PID, part III Assignment 2
(latex file)
Lecture 12k-ary n-ic maps, parametrizing cubic algebras over a PID, part I
Lecture ?? Assignment 3
(latex file)
Last modified: 10th of November, 2017