Topic: Intersections of Macdonald theory, knot homology, and cluster algebras
Meetings: Wednesdays 2:30-4pm in East Hall 4096 (NOTICE THE NEW ROOM!)
Organizers: Sunita Chepuri, Thomas Lam, George Seelinger, Melissa Sherman-Bennett
Winter Semester Calendar
Date
1/26/22
2/2/22
2/9/22
2/16/22
2/23/22
3/9/22
3/16/22
3/23/22
3/30/22
4/6/22
4/13/22
Speaker
Linh Truong
Thomas Lam
Katie Waddle
Zenan Fu
Terrence George
Scott Neville
Amanda Schwartz
David Speyer
Sunita Chepuri
George Seelinger
Melissa Sherman-Bennett
Topic
Grid homology
Introduction/Overview
Quivers and Plabic Graphs
Cluster Algebras and Cluster Varieties
Positroid Varieties
Cohomology of Cluster Varieties I
Positroid Links
Cohomology of Cluster Varieties II
Introduction to Braid Varieties
Braid Varieties and Positroids
Toric charts in braid varieties
Fall Semester Calendar
Date
9/15/21
9/22/21
9/29/21
10/6/21
10/13/21
10./20/21
10/27/21
11/3/21
11/10/21
11/17/21
12/1/21
12/8/21
Speaker
Melissa Sherman-Bennett
Sunita Chepuri
Will Dana
Katie Waddle/David Speyer
Yutong Li
Terrence George
Amanda Schwartz
George Seelinger
Thomas Lam
Sunita Chepuri
Nir Gadish
George Seelinger
Topic
Introduction
Macdonald Polynomials
HOMFLY I
q,t-Catalan Numbers/Macdonald Examples
HOMFLY II
Parking Functions and LLT Polynomials
HOMFLY and R-polynomials
The Shuffle Theorem
KR Link Homology
Torus Knot Link Homology
Torus Knot Link Homology
Torus Knot Link Homology
Resources
HOMFLY of torus links: Jones, Hecke algebra representations of braid groups and link polynomials
Catalan numbers: https://www.math.ucla.edu/~pak/lectures/Cat/pakcat.htm
q,t-Catalan numbers: https://www2.math.upenn.edu/~jhaglund/books/qtcat.pdf
Shuffle Theorem: https://www.ams.org/journals/bull/2020-57-01/S0273-0979-2019-01672-3/S0273-0979-2019-01672-3.pdf
Connections to knot invariants: https://www2.math.upenn.edu/~jhaglund/preprints/IMAfinal.pdf