Knot Number Theory Seminar
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
Each week someone may volunteer to lecture on material from the above primary source.
(Topics subject to change based on interest.)
Friday, March 31st
Andrew Tawfeek will provide an overview and lecture on knot groups.
Friday, April 7th
Alex Wang will lecture on quadratic reciprocity.
Friday, April 14th
Joeseph Rogge will lecture on ramified covering spaces.
Friday, April 21st
Alex Wang will lecture on number rings and etale coverings.
Friday, April 28th
Andrew Tawfeek will lecture on linking numbers.
Friday, May 5th
Ting Gong will lecture on etale fundamental groups.
Friday, May 12th
Alex Wang will lecture on p-adic integers and prime groups.
Friday, May 26th
Andrew Tawfeek will lecture on Alexander polynomials.