Time and Place. We will meet every MTWR at 9:00am in Hurley 258. We will meet most days at 1:00pm in the same room for problem solving sessions.
Textbook. Knots and Links by Peter Cromwell.
Mentors. Mitchell Faulk (mitchellmfaulk at gmail.com) and Jack Burkart (jburkart26 at gmail.com)
Office Hours. 10:00am-11:30am (Mitchell) and 2:30pm-4:00pm (Jack)
Office Location. Hayes-Healy 220
References. Below I'll list additional references.
Tex. Kevin provided us with his awesome homework template.
Below is the schedule and syllabus, which is likely optimistic. You can sign up to give a lecture here.
| Day | Topic(s) | Sections | Speaker(s) | Notes | Problems |
|---|---|---|---|---|---|
| M June 1 | Preliminaries, knots, knot type | 1.1,1.2 | Mitchell | Lecture 1 Notes | Problem Set 1 |
| T June 2 | Polygonal knots, smooth knots, torus knots | 1.3, 1.4, 1.5 | Jack | ||
| W June 3 | Lissajous knots, reverse, reflection | 1.6,1.7 | Ben Gunning | Problem Set 2 | |
| R June 4 | Links, link invariants, locally flat, and tame knots | 1.8, 1.9, 1.11 | Ben Hallberg | ||
| M June 8 | 3-sphere, manifolds | 2.1, 2.2 | Jack | Lecture 5 Notes | Problem Set 3 |
| T June 9 | Orientation, Euler characteristic, and surfaces | 2.3, 2.6, 2.7 | Mitchell | Lecture 6 Notes | |
| W June 10 | Graphs, the combinatorial approach | 2.11, 2.12 | Mike McCaffrey | Lecture 7 Notes | |
| R June 11 | Projections, link diagrams and their properties | 3.1, 3.2, 3.3 | Kevin Latimer | Lecture 8 Notes | |
| M June 15 | Crossing number | 3.5 | Jeff Marino | Problem Set 4 | |
| T June 16 | Invariants from oriented diagrams, Reidemeister moves | 3.6, 3.7, 3.8 | Matthew | ||
| W June 17 | Split links, Satellites | 4.1, 4.2, | Tallis Bowers | Lecture 11 Notes | Problem Set 5 |
| R June 18 | Factorizing links, Prime satellites | 4.3, 4.4 | Andrew Jena | Lecture 12 Notes | |
| M June 22 | Uniqueness of factorization (outline), product operation | 4.5, 4.6 | Ben Gunning | Lecture 13 Notes | |
| T June 23 | Link invariants and factorization, tangle decomposition | 4.7, 4.9 | Kevin Latimer | ||
| W June 24 | Bridge presentation | 4.10 | Matthew | Problem Set 6, Solutions | |
| R June 25 | Genus, Seifert surface | 5.0, 5.1 | Greg Greif | ||
| M June 29 | Seifert graph, genus 1 knots | 5.2, 5.3 | Greg Greif | Problem Set 7 | |
| T June 30 | Genus and factorization | 5.6 | Andrew Jena | Lecture 18 Notes | |
| W July 1 | Loops in graphs, | 6.1 | Tallis Bowers | Lecture 19 Notes | |
| R July 2 | Extra Day | ||||
| M July 6 | Simplicial complexes and their loops | 6.2, 6.3 | Pedro Soto | Problem Set 8 | |
| T July 7 | Homology of surfaces | 6.4 | Pedro Soto | ||
| W July 8 | Seifert matrix and invariants | 6.5, 6.6 | Mike | Lecture 22 Notes | |
| R July 9 | Properties of signature and determinant | 6.7 | Mike McCaffrey | Problem Set 9, Solutions | |
| M July 13 | Signature and unknotting number | 6.8 | Jeff Marino | ||
| T July 14 | Alexander polynomial | 7.1 | Ben Hallberg | Problem Set 10 | |
| W July 15 | Alexander polynomial and genus, skein relation | 7.2, 7.3 | Andrew Jena | Lecture 26 Notes | |
| R July 16 | Conway polynomial | 7.4 | Jeff Marino | ||
| M July 20 | Kauffman bracket | 9.1, 9.2 | Ben Gunning | ||
| T July 21 | Properties of bracket polynomial | 9.3 | Tallis Bowers | ||
| W July 22 | Khovanov Homology | Mitchell | Lecture 30 Notes |