HU Credits: 3

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: English

Campus: E. Safra

Course/Module Coordinator: Ari Shnidman

Coordinator Email: ariel.shnidman@mail.huji.ac.il

Coordinator Office Hours:

Teaching Staff:
Dr. Schneidman Ari

Course/Module description:
The goal of the course will be to survey the field of arithmetic statistics. We will begin by studying statistical questions related to number fields, such as how many are there? and what is the average size of their class groups? The second half of the course will focus on rational points of elliptic curves and curves of higher genus as well.

Course/Module aims:

Learning outcomes - On successful completion of this module, students should be able to:
The goal will be to spark interest in the area. Over the course of the semester I will suggest several independent research projects. By the end of the semester the students should have the tools to start solving these problems, if they choose to do so.

Attendance requirements(%):

Teaching arrangement and method of instruction:

Course/Module Content:
Counting number fields of bounded discriminant, Malle's conjecture, geometry-of-numbers, Bhargava's work, Cohen-Lenstra heuristics, average size of n-torsion in the class group, rational points on elliptic curves, Mordell's theorem, Selmer groups, Goldfeld's conjecture, arithmetic invariant theory

Required Reading:
Course notes.
A prior or parallel course in algebraic number theory would be helpful, but not strictly necessary. Similarly, some exposure to basic algebraic geometry will be helpful, but not expected.

Additional Reading Material:

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 100 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information: