Location: IHP, room 201

The talks are broadcasted via Zoom:

https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09

**10:45** Louis Ioos (Cergy Pontoise)** **** A Riemann-Roch formula for singular symplectic reductions.**

*Abstract:*Given a Hamiltonian action of a Lie group G on a symplectic manifold, the Quantization commutes with Reduction principle ([Q,R]=0) of Guillemin-Sternberg states that the space of G-invariants of the quantization of this manifold coincides with the quantization of its symplectic reduction by G. This principle provides in particular a geometric approach to the study of the representation theory of G. In this talk, I will consider the case where G is a circle and where the symplectic reduction is a compact singular symplectic space, then present an approach to establish this principle based on the Berline-Vergne formula and the asymptotics of the Witten integral. This talk is based on a joint work in collaboration with Benjamin Delarue and Pablo Ramacher.

**14:00** Russel Avdek (Orsay)

**Transverse stabilization in dim>3 contact topology.**

*We'll define stabilization for codimension 2 contact manifolds of dim>3 contact manifolds so that the following holds: A contact manifold is overtwisted iff its standard contact unknot (the dividing set of the boundary of a Darboux disk) is a stabilization. For n>1 we describe stabilized dim=2n-1 standard contact spheres inside of the dim=2n+1 standard sphere which are formally contact isotopic to standard contact unknots. These results build on work of Casals-Murphy-Presas and Casals-Etnyre, respectively. The proofs only use the differential topology of Weinstein manifolds and we'll aim for accessibility.*

Abstract:

Abstract:

**15:45**Yuan Yao (Jussieu/Orsay)

Symplectic packings in higher dimensions.

Symplectic packings in higher dimensions.

*Abstract*: The problem of symplectically packing k symplectic balls into a larger one has been solved in dimension four, i.e. there is now a combinatorial criteria of when this is possible. However, not much is known about symplectic packing problems in higher dimensions. We take a step in this direction in dimension six, by considering a “stabilized” packing problem, i.e. we consider symplectically packing a disjoint union of four dimensional balls times a closed Riemann surface into a bigger ball times the same Riemann surface. We show this is possible if and only if the corresponding four dimensional ball packing is possible. The proof is a mixture of geometric constructions, pseudo-holomorphic curves, and h-principles. This is based on work to appear with Kyler Siegel.

**Next Symplectix:**

1/12 (F. Loeser, I. Datta, P-A. Arlove)

**Other symplectic activity in Paris:**

**-**Séminaire Nantes-Orsay

- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time, first session of the year on Oct 13 with P. Seidel)