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

Announcements:

• First lecture: Tuesday, Aug. 22

Course material:

• Syllabus
• Assignment preamble latex file

Lecture 1	Introduction, motivation, and sieving for squarefree numbers
Lecture 2	Counting quadratic fields, interlude on Dirichlet series and Tauberian theorems (Source: Appendix of Ellenberg–Pierce–Wood)
Lecture 3	Malle's conjecture: precise statement and examples (Source: Malle's On the distribution of Galois groups, II)	Assignment 1 (latex file)
Lecture 4	Malle's heuristic reasoning, the Wirsing–Odoni method (Source: Malle loc. cit., Finch–Martin–Sebah, Prop. 4)
Lecture 5	Analytic part of counting cyclic cubics, some class field theory
Lecture 6	Conductors and discriminants, algebraic part of counting cyclic cubics
Lecture 7	Counting V4-quartics, part I
Lecture 8	Counting V4-quartics, part II
Lecture 9	Rings 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 10	Parametrizing quadratic algebras over a PID, part II
Lecture 11	Parametrizing quadratic algebras over a PID, part III	Assignment 2 (latex file)
Lecture 12	k-ary n-ic maps, parametrizing cubic algebras over a PID, part I
Lecture ??		Assignment 3 (latex file)