Geometry/Physics Seminar

Title: Rulings polynomials and augmentations of Legendrian links
Speaker: Dan Rutherford
Speaker Info: University of Arkansas
Brief Description:
Special Note:

Abstract: A normal ruling is a type of decomposition of the front diagram of a Legendrian knot in R^3 that arises when studying Legendrian knots via generating families or via Legendrian contact homology. Making a refined count of normal rulings allows the definition of a Legendrian link invariant known as the ruling polynomial that is a Laurent polynomial in a variable $z$. Another class of Legendrian invariants, the augmentation numbers, arise from making normalized counts of augmentations of the Legendrian contact homology DGA into finite fields. In this talk, I will present recent results that show augmentation numbers are determined by specializing the ruling polynomial via $z = q^{1/2}-q^{-1/2}$ where $q$ denotes the order of the corresponding finite field. As a corollary, we deduce that the ruling polynomial is determined by the Legendrian contact homology DGA. This is joint work with Brad Henry.
Date: Tuesday, October 29, 2013
Time: 4:00pm
Where: Lunt 107
Contact Person: Michael Couch
Contact email: mcouch@math.northwestern.edu
Contact Phone:
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