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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.
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