- 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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