Seminars and Colloquia by Series

SL3 Skein Algebras of Surfaces by Vijay Higgins

Series
Geometry Topology Seminar
Time
Monday, September 28, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Virtual
Speaker
Vijay Higgins – UC Santa Barbara –

The SL2 skein algebra of a surface is built from diagrams of curves on the surface. To multiply two diagrams, we draw one diagram on top of the other and then resolve the crossings with the Kauffman bracket. If we replace SL2 with another quantum group, we replace curves by embedded graphs on the surface. Recently, Thang Le showed that the SL2 skein algebra has a nice decomposition into simpler algebras whenever the surface has an ideal triangulation. This triangular decomposition is a powerful tool and should help us to study other skein algebras if we are able to show that the necessary ingredients exist. In this talk, I will explain what these ingredients are and how to find them for the SL3 skein algebra of trivalent webs on a surface.

8.3.3

The embedded contact homology of prequantization bundles

Series
Geometry Topology Seminar
Time
Monday, September 21, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
on line
Speaker
Morgan Weiler – Rice

The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base, the only known computation of ECH to date which does not rely on toric methods. We extend this result by computing the Z-grading on the chain complex, permitting a finer understanding of this isomorphism. We fill in some technical details, including the Morse-Bott direct limit argument and some writhe bounds. The former requires the isomorphism between filtered Seiberg-Witten Floer cohomology and filtered ECH as established by Hutchings--Taubes. The latter requires the work on higher asymptotics of pseudoholomorphic curves by Cristofaro-Gardiner--Hutchings—Zhang.

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