Home - Sikorav 60

Schedule

Thursday talks will take place at the Université Lyon 1. Friday and Saturday talks will take place at the ENS de Lyon.

François Laudenbach
What could be a de Rham theorem in the setting of the Morse-Novikov theory?

TBA.

Yakov Eliashberg
Simplifying singularities of Lagrangian skeleta

I discuss in the talk Nadler’s arborealization conjecture concerning singularities of skeleta of Weinstein manifolds, and the program for proving it based on our joint work with D. Nadler and L. Starkston.

Helmut Hofer
Feral Pseudoholomorphic Curves and Dynamics

In this talk I shall describe how a new class of pseudoholomorphic curves can be used to find minimal sets.

Stefan Nemirovski
Transverse families and generating hypersurfaces

Transverse families of Legendrians are a generalisation of positives loops. Generating functions techniques can be used to show that a transverse family in the Legendrian isotopy class of the fibre of a spherical cotangent bundle is never contractible. The talk is based on joint work with Vladimir Chernov.

Patrick Bernard
Fonctions de Lyapounov et fonctions temps

TBA.

Claude Viterbo
Sheaves and symplectic geometry

TBA.

Chris Wendl
Rigid holomorphic curves are generically super-rigid

I will explain the main ideas of a proof that for generic compatible almost complex structures in symplectic manifolds of dimension at least 6, closed embedded J-holomorphic curves of index 0 are always "super-rigid", implying that their multiple covers are never limits of sequences of curves with distinct images. This condition is especially interesting in Calabi-Yau 3-folds, where it follows that the Gromov-Witten invariants can be "localized" and computed in terms of Euler classes of obstruction bundles for a finite set of disjoint embedded curves. By the same techniques, we can also show that unbranched covers of simple J-holomorphic curves are generically regular. These results are based on a decomposition of the space of branched covers into smooth strata on which certain twisted Cauchy-Riemann operators have kernel and cokernel of constant dimension.

Lisa Traynor
Lagrangian Fillings of Legendrian Submanifolds

A classic question in knot theory is: Given a smooth knot in the 3-sphere, what surfaces in the 4-ball can it bound? In symplectic geometry, a natural question is: Given a Legendrian knot, what Lagrangian surfaces can it bound? Whereas any smooth knot can be filled by an infinite number of topologically distinct surfaces, there are classical and non-classical obstructions to the existence of Lagrangian fillings of Legendrian knots. In particular, a polynomial associated to the Legendrian through the technique of generating functions can show that there is no compatible embedded Lagrangian filling. Legendrians that admit generating functions will always admit compatible immersed Lagrangian fillings, and I will describe how this polynomial also gives information about the minimal number and indices of double points in compatible immersed Lagrangian fillings. In addition, I will describe some constructions to realize minimally immersed fillings. This is joint work with Samantha Pezzimenti.

Michel Boileau
Cyclic branched covers, L-spaces and quasipositive links

L-spaces are the class of 3-dimensional rational homology spheres for which the dimension of Heegaard Floer homology is the smalllest possible.In this talk we present some leading conjectures about L-spaces and discuss the case of cyclic covers of $S^3$ branched over links. For a strongly quasipositive knot in $S^3$ with monic Alexander polynomial, if the n-fold cyclic branched cover is a L-space we show that $n \leq 5$ and that the Alexander polynomial is a non-trivial product of cyclotomic polynomials. We also get applications to the determination of the smooth and topological 4-ball genera of some quasipositive knots. This is a Joint work with Steve Boyer (University of Quebec at Montreal) and Cameron McA. Gordon (University of Texas at Austin).

Jean-François Barraud
A Novikov fundamental group

Just like there might be homotopical constraints on the critical points of Morse functions that are not detected by the homology of the ambient manifold, closed $1$ forms may have necessary critical points that are not detected by the Novikov homology. I will present an agebraic invariant that captures some of this information, and is an analogue in Novikov theory to the fundamental group in Morse theory. In particular, this "Novikov fundamental group" leads to new lower bounds for the number of index $1$ and $2$ critical points of closed $1$-forms, that are essentially different from the Novikov inequalities. (joint with H.V. Le and A. Gadbled).

Mihai Damian
Lagrangian submanifolds and fibrations over the circle

Given a closed Lagrangian submanifold $L\subset M$ we investigate the conditions which imply that $L$ is the total space of a fibration over the circle, starting with the inspirational work of Jean-Claude Sikorav.

Thu 02	Fri 03	Sat 04
9:30 a.m.-10:30 a.m. François Laudenbach What could be a de Rham theorem in the setting of the Morse-Novikov theory?	9:30 a.m.-10:30 a.m. Yakov Eliashberg Simplifying singularities of Lagrangian skeleta	9:30 a.m.-10:30 a.m. Helmut Hofer Feral Pseudoholomorphic Curves and Dynamics
11 a.m.-noon Stefan Nemirovski Transverse families and generating hypersurfaces	11 a.m.-noon Patrick Bernard Fonctions de Lyapounov et fonctions temps	11 a.m.-noon Claude Viterbo Sheaves and symplectic geometry
2 p.m.-3 p.m. Chris Wendl Rigid holomorphic curves are generically super-rigid	1:30 p.m.-2:30 p.m. Lisa Traynor Lagrangian Fillings of Legendrian Submanifolds
3:30 p.m.-4:30 p.m. Michel Boileau Cyclic branched covers, L-spaces and quasipositive links	3 p.m.-4 p.m. Jean-François Barraud A Novikov fundamental group
	4:30 p.m.-5:30 p.m. Mihai Damian Lagrangian submanifolds and fibrations over the circle

Thu 02

9:30 a.m.-10:30 a.m. François Laudenbach
What could be a de Rham theorem in the setting of the Morse-Novikov theory?

François Laudenbach
What could be a de Rham theorem in the setting of the Morse-Novikov theory?

TBA.

11 a.m.-noon Stefan Nemirovski
Transverse families and generating hypersurfaces

Stefan Nemirovski
Transverse families and generating hypersurfaces

2 p.m.-3 p.m. Chris Wendl
Rigid holomorphic curves are generically super-rigid

Chris Wendl
Rigid holomorphic curves are generically super-rigid

3:30 p.m.-4:30 p.m. Michel Boileau
Cyclic branched covers, L-spaces and quasipositive links

Michel Boileau
Cyclic branched covers, L-spaces and quasipositive links

Fri 03

9:30 a.m.-10:30 a.m. Yakov Eliashberg
Simplifying singularities of Lagrangian skeleta

Yakov Eliashberg
Simplifying singularities of Lagrangian skeleta

11 a.m.-noon Patrick Bernard
Fonctions de Lyapounov et fonctions temps

Patrick Bernard
Fonctions de Lyapounov et fonctions temps

TBA.

1:30 p.m.-2:30 p.m. Lisa Traynor
Lagrangian Fillings of Legendrian Submanifolds

Lisa Traynor
Lagrangian Fillings of Legendrian Submanifolds

3 p.m.-4 p.m. Jean-François Barraud
A Novikov fundamental group

Jean-François Barraud
A Novikov fundamental group

4:30 p.m.-5:30 p.m. Mihai Damian
Lagrangian submanifolds and fibrations over the circle

Mihai Damian
Lagrangian submanifolds and fibrations over the circle

Sat 04

9:30 a.m.-10:30 a.m. Helmut Hofer
Feral Pseudoholomorphic Curves and Dynamics

Helmut Hofer
Feral Pseudoholomorphic Curves and Dynamics

In this talk I shall describe how a new class of pseudoholomorphic curves can be used to find minimal sets.

11 a.m.-noon Claude Viterbo
Sheaves and symplectic geometry

Claude Viterbo
Sheaves and symplectic geometry

TBA.

Symplectic Geometry in Lyon

A conference in honor of Jean-Claude Sikorav

Lyon, November 2nd-4th, 2017

Celebrating Jean-Claude's 60th birthday

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