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
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:
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 V_{4}quartics, part I 

Lecture 8  Counting V_{4}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  kary nic maps, parametrizing cubic algebras over a PID, part I  
Lecture ??  Assignment 3 (latex file) 