# Knot Number Theory Seminar

This is the homepage for the Knot Number Theory Reading Seminar focused on learning the basics of arithmetic topology.

This seminar is co-organized by Alex Galarraga (agalar@uw.edu) and myself (atawfeek@uw.edu) at the University of Washington.

This seminar ran for the Spring 2023 quarter.

## References

We will be primarily following these lecture notes.

A alternate standard reference is:

Knots and Primes: An Introduction to Arithmetic Topology by Masanori Morishita

For references on algebraic topology and number theory:

Algebraic Topology by Allen Hatcher

The Knot Book by Colin Adams

Primes of the form x^2 + ny^2: Fermat, Class Field Theory, and Complex Multiplication, by David Cox

A Course in Arithmetic by J-P. Serre

Number Theory 1: Fermat's Dream, Number Theory 2: Introduction to Class Field Theory by Kazuya Kato, Nobushige Kurokawa and Takeshi Saito

## Schedule:

Each week someone may volunteer to lecture on material from the above primary source.

(Topics subject to change based on interest.)

### Lecture 1:

Friday, March 31st

Andrew Tawfeek will provide an overview and lecture on knot groups.

### Lecture 2:

Friday, April 7th

Alex Wang will lecture on quadratic reciprocity.

### Lecture 3:

Friday, April 14th

Joeseph Rogge will lecture on ramified covering spaces.

### Lecture 4:

Friday, April 21st

Alex Wang will lecture on number rings and etale coverings.

### Lecture 5:

Friday, April 28th

Andrew Tawfeek will lecture on linking numbers.

### Lecture 6:

Friday, May 5th

Ting Gong will lecture on etale fundamental groups.

### Lecture 7:

Friday, May 12th

Alex Wang will lecture on p-adic integers and prime groups.

### Lecture 8:

Friday, May 26th

Andrew Tawfeek will lecture on Alexander polynomials.