The 7^th Workshop for Young Symplectic Geometers

Invited Speakers

	February 23 (Fri)	February 24 (Sat)	February 25 (Sun)
09:50 – 10:00	Arrival and Registration	Opening Remark
10:00 – 10:50		H. Jung (I)	Y. Cho (II)
10:50 – 11:10		Break
11:10 – 12:00		D. Cho (I)	H. Jung (III)
12:00 – 14:00		Lunch
14:00 – 14:50		Y. Cho (I)	D. Cho (III)
14:50 – 15:10		Break
15:10 – 16:00	Free Discussion	H. Jung (II)	Y. Cho (III)
16:00 – 16:10		Break	Free Discussion & Question Session
16:10 – 17:00		D. Cho (II)
17:00 – 18:00		Free Discussion
18:00 –		Workshop Dinner	Departure

* The schedule may vary.

Speaker: Dahye Cho (Yonsei University)
Title: Introduction to (Relative) Symplectic Cohomology and Applications
Abstract: For certain non-compact symplectic manifold with nice properties, we can apply Morse theory on the space of loops on the symplectic manifold, following Floer’s idea. In this talk, we will review definitions of symplectic cohomology, its relative version, and some geometric properties of them. There is a spectral sequence relating two versions of symplectic cohomology via the winding filtration. I will briefly explain the main idea of constructing the spectral sequence and provide applications to detect cylindrical affine varieties.

Speaker: Yunhyung Cho (Sungkyunkwan University)
Title: Maximal tori in the Hamiltonian diffeomorphism group
Abstract: Let $M$ be a compact symplectic toric manifold. It is known by McDuff that the number of maximal tori is finite up to conjugation by elements of symplectomorphism groups. She also posed an interesting conjecture whether the number is one when a symplectic form is monotone. Recently, this conjecture was solved in some special classes of manifolds such as Bott manifolds or small / large Picard numbers. In this talk, I will introduce two ideas to approach this problem: (1) c_1-cohomological rigidity of Fano manifolds (by C.-Lee-Masuda-Park) and (2) mutations of polytopes (Pabiniak-Tolman).

Speaker: Hongtaek Jung (Seoul National University)
Title: Symplectic structure on Hitchin components
Abstract: Let $S$ be a closed orientable surface of genus $g>1$. We introduce the $\operatorname{PSL}(n,\mathbb{R})$-Hitchin component sitting inside the character variety $\operatorname{Hom}(\pi_1(S),\operatorname{PSL}(n,\mathbb{R}))/\operatorname{PSL}(n,\mathbb{R})$ and discuss its smooth and symplectic structure. In the second half of the talk, we show that $\operatorname{PSL}(3,\mathbb{R})$-Hitchin component is symplectomorphic to the standard Euclidean space.