# A Celebration of Symplectic Geometry: 15 Years of JSG, June 5-6, 2017

In celebration of the Journal of Symplectic Geometry’s 15th anniversary, the Center of Mathematical Sciences and Applications will be hosting A Celebration of Symplectic Geometry: 15 Years of JSG on June 5-6, 2017.

Confirmed speakers:

The conference is co-organized by Denis Auroux and Victor Guillemin. Additional information on the conference will be announced closer to the event.

### Schedule:

#### June 5, Monday (Full day)

 Time Speaker Topic 8:30am – 9:0am Breakfast 9:00am – 10:00am Jonathan Weitsman 10:30am – 11:30am Eckhard Meinrenken Title: On Hamiltonian loop group spaces Abstract: Let $G$ be a compact Lie group, and $\mathcal{M}$ a Hamiltonian space for the loop group $LG$, with proper moment map. We explain a construction of an $LG$-equivariant spinor module over $\mathcal{M}$, which may be regarded as the canonical spin-c structure for the infinite-dimensional manifold $\mathcal{M}$. We show how to reduce to finite dimensions, resulting in a “twisted spin-c structure” for the associated quasi-hamiltonian $G$-space $M$. This is based on joint work with Yiannis Loizides and Yanli Song. 11:30am – 1:30pm Break 1:30pm – 2:30pm Ana Rita Pires Title: Infinite staircases in symplectic embedding problems Abstract: McDuff and Schlenk studied an embedding capacity function, which describes when a 4-dimensional ellipsoid can symplectically embed into a 4-ball. The graph of this function includes an infinite staircase related to the odd index Fibonacci numbers. Infinite staircases have been shown to exist also in the graphs of the embedding capacity functions when the target manifold is a polydisk or the ellipsoid E(2,3). I will describe how we use ECH capacities, lattice point counts and Ehrhart theory to show that infinite staircases exist for these and a few other target manifolds, as well as to conjecture that these are the only such target manifolds. This is a joint work with Cristofaro-Gardiner, Holm and Mandini. 3:00pm – 4:00pm Sobhan Seyfaddini 4:30pm – 5:30pm Roger Casals Title: Differential Algebra of Cubic Graphs Abstract: In this talk we will associate a combinatorial dg-algebra to a cubic planar graph. This algebra is defined by counting binary sequences, which we introduce, and we shall provide explicit computations and examples. From there we study the Legendrian surfaces behind these constructions, including Legendrian surgeries, the count of Morse flow trees involved in contact homology, and the relation to microlocal sheaves. Time permitting, I will explain a connection to spectral networks.

June 6, Tuesday (Full day)

 Time Speaker Topic 8:30am – 9:00am Breakfast 9:00am – 10:00am Alejandro Uribe 10:30am – 11:30am Alisa Keating Title: Symplectomorphisms of exotic discs Abstract: 11:30am – 1:30pm Break 1:30pm – 2:30pm Chen He 3:00pm – 4:00pm Yael Karshon