Upcoming Seminars:
• Monday, September 30, 2019, 3:15pm, 119 Physics, Triangle Topology Seminar
DGA Representations, Ruling Polynomials, and the Colored HOMFLY-PT Polynomial
Caitlin Leverson (Georgia Tech)

Given a pattern braid $\beta\in J^1(S^1)$, to any Legendrian knot $\Lambda$ in $\mathbb{R}^3$ with the standard contact structure, we can associate the Legendrian satellite knot $S(\Lambda,\beta)$. We will discuss the relationship between counts of augmentations of the Chekanov­Eliashberg differential graded algebra of $S(\Lambda,\beta)$ and counts of certain representations of the algebra of $\Lambda$. We will then define an $m$­graded $n$­colored ruling polynomial from the $m$­graded ruling polynomial, analogously to how the $n$­colored HOMFLY­PT polynomial is defined from the HOMFLY­PT polynomial, and extend results of the second author, to show that the $2$­graded $n$­colored ruling polynomial appears as a specialization of the $n$­colored HOMFLY­PT polynomial. This is joint work with Dan Rutherford.

• Monday, October 28, 2019, 3:15pm, 119 Physics, Triangle Topology Seminar
TBA
Tom Hockenhull (University of Glasgow, Mathematics)

• Monday, November 11, 2019, 3:15pm, 119 Physics, Triangle Topology Seminar
TBA
Arunima Ray (Max Planck Institute for Mathematics)

• Monday, December 2, 2019, 3:15pm, 119 Physics, Triangle Topology Seminar
TBA
Maggie Miller (Princeton University, Mathematics)

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