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Geometry and Topology Seminars

2020 Geometry and Topology Seminars

The main organizer of these seminars is Prof. Ronan Conlon, rconlon@fiu.edu

 

Classical invariants of Legendrian knots.

Speaker:  Ivan Yakovlev from HSE and Skoltech, Moscow.
Time: Wednesday 2/5/2020 at 1pm-2pm.  
Room:  DM 409A

Abstract: In my talk I will give a brief introduction to Legendrian knots. I will recall the basic results from contact geometry and define the rotation number and the Thurston-Bennecken number (combinatorially and topologically), then formulate several classification results about knots in tight contact manifolds. Then I will describe  the Chekanov example of Legendrian non-isotopic knots with the same classical invariants, which largely determined the development of contact geometry in the last two decades

Laplacian eigenspectra and geometric quantization of Riemannian Symmetric Spaces

Speaker: PhD student Camilo Montoya  
Time: Friday 09/27/2019 at 1:30pm-2:30pm. Continuing on Fridays through at least 11/8.  
Room:  DM 409A

Abstract: In this talk we review the basics of symmetric spaces, and study them via the theory of Lie groups and Lie algebras. We show how the symplectic quotient and geometric quantization of a compact Riemannian symmetric space can be identified with generalized flag manifolds, which can also be thought of as the geodesic flow of the space (at least for the rank 1 case). We outline the recent results by D. Grantcharov and G. Grantcharov in the rank 1 case, and if time permits, if not the next talk, the future work along these lines for maximal rank symmetric spaces.