Location: IHP, room 201
The talks are broadcasted via Zoom:
https://zoom.us/j/89445897442?pwd=QmVZWHBiM2Nwb09yUVJERnYrSHJrUT09
10:45 David Bechara Senior (Aachen)
The asymptotic action of area preserving disk maps and some of its properties.
Abstract: Given a diffeomorphism of the disk that preserves the standard symplectic form, I will introduce the asymptotic action associated to this map. I will then show a pointwise formula relating the asymptotic action to the asymptotic winding number of pairs of points. As a corollary one obtains a generalization for a well known result by A. Fathi which gives a formula for the Calabi invariant of a disk map in terms of its mean winding numbers. Additionally I will focus on how this formula can be used to study symplectic dynamical information for irrational pseudo-rotations of the disk. This talk includes joint work with Patrice Le Calvez and Abror Pirnapasov.
14:00 Yanki Lekili (London)
New orders associated with terminal threefold singularities.
Abstract: This is based on joint work with Jenia Tevelev. I will tell you a story of a vector bundle due to Kawamata that captures the "categorical essence" of certain terminal 3-fold singularities. Our computations are done in the mirror via Floer theory but it teaches us (with a proof!) something new about derived categories of terminal threefold singularities and noncommutative algebra by providing explicit deformations of the so-called Kalck-Karmazyn algebra associated with cyclic quotient surface singularities.
15:45 Salammbo Connolly (Orsay)
On torsion in (bi)linearized Legendrian contact homology.
Abstract: Given a Legendrian submanifold in a contact manifold, one can define its
Legendrian Contact Homology (LCH). This invariant is unfortunately
difficult to compute. However, there exist two more computable variants,
linearized LCH (defined by Chekanov), and bi-linearized LCH (defined by
Bourgeois and Chantraine). For legendrian knots in R^3, very little is
known about the possibility of having torsion in these invariants when
they are defined over integer coefficients. In joint work with Frédéric
Bourgeois, we give properties of torsion that can appear in linearized
LCH with integer coefficients, and also give the full geography of
bi-linearized LCH with integer coefficients.
Next Symplectix:
26/04 (Coté, Ward, Dimitroglou-Rizell)
Other symplectic activity in Paris:
- Mini-course of Shaoyun Bai in the week 11/03-14/03
- Séminaire Nantes-Orsay
- Symplectic Zoominar (every Fridays except Symplectix' Fridays at 15:15, Paris time)
