Welcome to the summer tutorial Knots and Primes. Chao and Charmaine are excited to share with you this piece of beautiful and surprising story of mathematics. Hope you have fun in exploring some analogy between knots and primes this summer!
Time: We will meet from July 2 (Mon) to August 11 (Fri), MWF 7pm-8pm. With the exception of the first week due to Independence Day: we will have no meeting on July 4 but will have two 1.5-hour meetings on July 2 and July 6, 7pm-8:30pm.
Location: Science Center 109.
Textbook: Masanori Morishita, Knots and Primes: An Introduction to Arithmetic Topology, Springer 2012. Each enrolled student has a $120 budget for books.
Recommended references on algebraic topology and number theory:
Check out the syllabus!
Lecture Notes in one file (Updated 2022/01/03, thank Xiaoxiang Zhou for a list of typos)
|1||07/02/2012||Charmaine Sia||Overview and Knot groups|
|2||07/06/2012||Chao Li||Quadratic reciprocity|
|3||07/09/2012||Charmaine Sia||Covering spaces|
|4||07/11/2012||Chao Li||Number rings and etale coverings|
|5||07/13/2012||Charmaine Sia||Linking numbers|
|6||07/16/2012||Chao Li||Etale fundamental groups|
|7||07/18/2012||Chao Li||More etale fundamental groups|
|8||07/20/2012||Chao Li||p-adic integers and prime groups|
|9||07/23/2012||Charmaine Sia||Alexander polynomials|
|10||07/25/2012||Charmaine Sia||More Alexander polynomials|
|11||07/27/2012||Chao Li||Class field theory|
|12||07/30/2012||Charmaine Sia||Asymptotic formulas on homology groups|
|13||08/01/2012||Chao Li||Ideal class groups|
|14||08/03/2012||Chao Li||Iwasawa theory|
Chao and Charmaine are glad to try our best to help you on the projects. Simply send us an email if you need any.
|08/06/2012||Allen Yuan||Braid groups|
|08/08/2012||Michael Jemison||Milnor invariants and multiple residue symbols|
|08/08/2012||Seth Neel||Genus theory of binary quadratic forms|
|08/10/2012||Arpon Raksit||Jones polynomial and Khovanov homology|
|08/10/2012||Jacob Postema||Homology groups and class groups|