Seminars and Colloquia by Series

An algorithm for comparing Legendrian links

Series
Geometry Topology Seminar
Time
Wednesday, October 18, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ivan Dynnikov – Steklov Mathematical Institute –

The talk is based on my joint works with Maxim Prasolov and Vladimir Shastin, where we studied the relation between rectangular diagrams of links and Legendrian links. This relation allows for a complete classification of exchange classes of rectangular diagrams in terms of equivalence classes of Legendrian links and their symmetry groups. Since all rectangular diagrams of given complexity can be searched, this yields a method to algorithmically compare Legendrian links. Of course, the general algorithm has too high complexity for a practical implementation, but in some situations, the most time consuming parts can be bypassed, which allows us to confirm the non-equivalence of Legendrian knots in several previously unresolved cases.

The Giroux correspondence in dimension 3

Series
Geometry Topology Seminar
Time
Monday, September 25, 2023 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joseph Breen – University of Iowa –

I will discuss recent work with K. Honda and Y. Huang on proving the Giroux correspondence between contact structures and open book decompositions. Though our work extends to all dimensions (with appropriate adjectives), this talk will focus on the 3-dimensional proof. I will first recall Giroux’s argument for existence of supporting open book decompositions, formulating it in the language adapted to our proof. The rest of the talk will be spent describing the proof of the stabilization correspondence.

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