Three 20 Minute Research Talks

Three 20 Minute Research Talks

Jesse Huang ,UIUC,   Shaoyun Bai, Princeton University,   Thomas Melistas, UGA

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Jesse Huang (UIUC), Variation of FLTZ skeleta

In this short talk, I will discuss an interpolation of FLTZ skeleta mirror to derived equivalent toric varieties. This is joint work with Peng Zhou.                                                                                                                                                            

Shaoyun Bai, Princeton University, SU(n)–Casson invariants and symplectic geometry 

In 1985, Casson introduced an invariant of integer homology 3-spheres by counting SU(2)-representations of the fundamental groups. The generalization of Casson invariant by considering Lie groups SU(n) has been long expected, but the original construction of Casson encounters some difficulties. I will present a solution to this problem, highlighting the equivariant symplectic geometry and Atiyah-Floer type result entering the construction.

 Thomas Melistas, UGA, The Large-Scale Geometry of Overtwisted Contact Forms

Inspired by the symplectic Banach-Mazur distance, proposed by Ostrover and Polterovich in the setting of non-degenerate starshaped domains of Liouville manifolds, we define a distance on the space of contact forms supporting a given contact structure on a closed contact manifold and we use it to bi-Lipschitz embed part of the 2-dimensional Euclidean space into the space of overtwisted contact forms supporting a given contact structure on a smooth closed manifold.