UU – Nantes Workshop on Lagrangian cobordisms and Floer theory

General information

Receipts and tickets: For those arriving from outside of Uppsala, please save transportation receipts for later reimbursements.

Arlanda Airport to Uppsala: The local public transport UL has both trains and buses from Arlanda to Uppsala central station. External guests are staying the first night at Elite Hotel Academia https://goo.gl/maps/F8ne2ReL7QbQunyz6 which is located right by the central station in Uppsala.

The venue: The workshop will be held at Haga slott, roughly one hour from Uppsala, where we will be staying Friday-Sunday with full boarding. For those who travel from Uppsala we will arrange transportation at 9 am from Stationsgatan, bus stop E.3 (Bus company: Högbergs Buss), near Elite Hotel Acadmeia: see https://goo.gl/maps/qLvFHjgzhBpm8rwr9 Those who arrange the travel themselves should save receipts.

From the venue to Arlanda Airport: We will arrange taxis and shuttles from Haga slott directly to both Arlanda and Uppsala on Sunday, depending on your needs.

Covid19 testing: For those who need an antigen/PCR test before leaving Sweden, you should book a test in advance at Arlanda airport https://reseintyg.vaccina.se/en/tidsbokning/#/service The company Vaccina has a reception in Clarion Hotel, Arlanda. Be sure to book it in advance and allocate sufficient time before the departure.

Further questions: Contact georgios.dimitroglou@math.uu.se

Schedule

Friday 8/10	Saturday 9/10	Sunday 10/10
09:00: Bus from Uppsala Central station	08:00-09:00 Breakfast	08:00-09:00 Breakfast
10:00 - 11:00 Coffee 11:00 - 12:30 GOLOVKO	09:00-10:30 EKHOLM 10:30-11:00 Coffee 11:00-12:30 MAK	09:00-10:30 COURTE 11:00-12:30 AVDEK
12:45 - 13:45 Lunch	12:30-13:30 Lunch 13:30-15:00 Discussions/Excursion	12:30-13:30 Lunch
13:45 - 15:15 GHIGGINI 15:15 - 15:30 Coffee 15:30 - 17:00 HICKS 17:00 - 18:30 GADBLED	15:00-15:30 Coffee 15:30-17:00 OANCEA 17:00-18:30 ZHANG	14:00 Bus going back to Uppsala Central station. (Taxis will be arranged for those who leave directly to Arlanda.)
18:45 Dinner	18:45 Dinner

Confirmed speakers

AVDEK,Russell

Title: An algebraic generalization of Giroux's criterion'

COURTE, Sylvain

Title: Twisted generating functions and the nearby Lagrangian conjecture

OANCEA, Alexandru

Title: Bialgebra structure on Rabinowitz Floer homology

EKHOLM, Tobias

Title: DG-algebras and singular Lagrangian cobordisms

GADBLED, Agnès

Title: Weinstein handlebodies for complements of smoothed toric divisors

GHIGGINI, Paolo

Title: A local mirror functor from singular Lagrangian submanifolds.

From time to time it happens to hear in talks a statement like "Floer homology is not possible in the presence of negative ends" or "a Floer thoery for singular Lagrangians does not exist". These statements are false: the SFT framework of Eliashberg-Givental-Hofer allows us to define Floer homology for Lagrangian submanifolds with negative ends (and therefore for Lagrangians with conical singularities) as a dg-module over the the Chekanov-Eliashberg dga of the concave end. This construction has been known to some experts for a very long time, and the details are spelled out in an article of Chantraine, Dimitroglou Rizell, Ghiggini and Golovko (where the existence of an augmentation for the negative end is assumed).

In my talk I will explain how an exact Lagrangian with a conical singularity in a Liouville manifold defines an A_\infty functor from the wrapped Fukaya category to the dg-modules over the Chekanov-Eliashberg algebra of the link of the singularity and discuss the explicit case of the core of C^3 - {xyz=1}, where the homology of the dga can be computed explicitly and turns out to be isomorphic to the coordinate ring of the mirror.

This is a joint work with Georgios Dimitroglou Rizell.

GOLOVKO, Roman

Title: Subloose Legendrian tori from Bohr-Sommerfeld covers of monotone Lagrangian tori

Abstract: By a result due to Ziltener, there exist no closed embedded Bohr-Sommerfeld Lagrangians inside CP^n for the prequantisation bundle whose total space is the standard contact sphere. On the other hand, any embedded monotone Lagrangian torus has a canonical nontrivial cover which is a Bohr-Sommerfeld immersion. We draw the front projections for the corresponding Legendrian lifts inside a contact Darboux ball of the threefold covers of both the two-dimensional Clifford and Chekanov tori (the former is the Legendrian link of the Harvey-Lawson special Lagrangian cone), and compute the associated Chekanov-Eliashberg algebras. Although these Legendrians are not loose, we show that they both admit exact Lagrangian cobordisms to the loose Legendrian sphere; they hence admit exact Lagrangian caps in the symplectisation, which are non-regular Lagrangian cobordisms.

In addition, we will discuss the conjecture relating superpotential of an embedded monotone Lagrangian two-torus in CP2 with the augmentation polynomial of the Legendrian lift of its canonical threefold Bohr-Sommerfeld cover. This is joint work with Georgios Dimitroglou Rizell.

HICKS, Jeff

Title: Speculation on Floer theory of Lagrangian cobordisms via decomposition

Abstract: Biran and Cornea proved that when K is a monotone Lagrangian cobordism with Lagrangian ends, the Floer cohomology of K is a mapping cocylinder yielding an equivalence between the Floer cohomology of the ends. In this talk, we will discuss how to decompose Lagrangian cobordisms with Lagrangian ends into Lagrangian surgery handles. We then speculate how one would use such a decomposition to provide criteria for when the Lagrangian K is an unobstructed object (in the sense of admitting a bounding cochain). Time permitting, we'll discuss how the same techniques might recover Biran and Cornea's result for unobstructed Lagrangian cobordisms with Lagrangian ends.

MAK, Cheuk Yu

Title: Lagrangian Floer theory and a simplicity problem

Abstract: It is a classical and fundamental problem to study algebraic properties of the automorphism group of an object, for example, the simplicity of the group. There are a lot of studies in the 60s and 70s in this direction for the automorphism group of compact (smooth) manifolds, possibly equipped with additional structures. When it comes to the volume preserving homeomorphism group, surprisingly, the higher dimensional cases are well-studied and the 2 dimensional case is more mysterious. Daniel Cristofaro-Gardiner, Vincent Humili`ere and Sobhan Seyfaddini have recently made a breakthrough for the 2-disc using periodic Floer homology. In this talk, I will explain a technically simpler approach using Lagrangian Floer theory on symmetric products (a slight variant of knot Floer homology), which completely resolves the simplicity problem for all surfaces. This is based on a joint work with Daniel Cristofaro-Gardiner, Vincent Humili`ere, Sobhan Seyfaddini and Ivan Smith.

ZHANG, Bingyu

Title: Capacities from the Chiu-Tamarkin complex