Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar
Three 20 Minute Research Talks
Yan-Lung Leon Li : Equivariant Lagrangian Correspondence and a Conjecture of Teleman
It has been a continuing interest, often with profound importance, in understanding the geometric and topological relationship between a Hamiltonian G-manifold Y and a symplectic quotient X. In this talk, we shall provide precise relations between their (equivariant) Lagrangian Floer theory. In particular, we will address a conjecture of Teleman, motivated by 3d mirror symmetry, on the 2d mirror construction of X from that of Y, which generalises Givental-Hori-Vafa mirror construction for toric varieties. The key technical ingredient is the Kim-Lau-Zheng’s equivariant extension of Fukaya’s Lagrangian correspondence tri-modules over equivariant Floer complexes. Joint work with Siu-Cheong Lau and Naichung Conan Leung.
- Levin Maier (Heidelberg) : TBA,
Austin Christian : Persistent Legendrian Contact Homology
This talk will report on an REU whose goal was to introduce the notion of persistence into Legendrian contact homology. The LCH of a Legendrian knot is computed as the homology of the knot's Chekanov-Eliashberg DGA and is a well-studied invariant of Legendrian isotopy types. For a given Legendrian embedding, the Chekanov-Eliashberg DGA admits a natural filtration, allowing for the computation of persistent homology. The purpose of this REU was to initiate the study of the resulting filtered homology. The project was joint with M. Basu, E. Clayton, D. Irvine, F. Mooers, and W. Shen.