Uppsala-Odense Geometry Days 24-25 October 2024

Venue: We will stay at Krusenberg Herrgård on 24-25 October located by the lake Ekoln. This is also where the workshop, lunches, and dinner will take place.

We will take a bus "Kristian Larsson Busstrafik" that leaves from Hotel Svava at 08:45 on Thursday 24 October.

Schedule

Participants

Santiago Achig (Uppsala University)
Russell Avdek (Sorbonne Université)
Peleg Bar-Lev (Uppsala University)
Joël Beimler (University of Southern Denmark)
Johan Björklund (University of Gävle)
Martin Bäcke (Uppsala University)
Guillem Cazassus (University of Southern Denmark)
Baptiste Chantraine (Nantes Université)
Adrien Currier (Nantes Université)
Georgios Dimitroglou Rizell (Uppsala University)
Luís Diogo (Uppsala University)
Milica Ðukić (Uppsala University)
Zhen Gao (Augsburg University)
Ezra Getzler (Uppsala University)
Paolo Ghiggini (Université Grenoble Alpes)
Roman Golovko (Charles University)
Tobias Ekholm (Uppsala University)
Malcolm Fack (Uppsala University)
Cecilia Karlsson (University of Borås)
Thomas Kragh (Uppsala University)
Guillaume Laplante-Anfossi (University of Southern Denmark)
Lionel Lang (University of Gävle)
Florent Le Borgne (Nantes Université)
Rémi Leclercq (Université Paris-Saclay)
Noémie Legout (University of Gävle)
Yin Li (Uppsala University)
Jing Liu (Université Grenoble Alpes)
Lisa Lokteva (Uppsala University)
Irena Matkovič (Uppsala University)
Yuki Matsubara (University of Southern Denmark)
Lukas Nakamura (Uppsala University)
Sunghyuk Park (Harvard University)
Adrian Petr (University of Southern Denmark)
Johan Rydholm (Uppsala University)
Matthias Scharitzer (University of Southern Denmark)
Vivek Shende (University of Southern Denmark)
Maksim Stokić (Uppsala University)
Filip Strakoš (Uppsala University)
Alex Takeda (Uppsala University)
Bingyu Zhang (University of Southern Denmark)

Abstracts

Speaker: Guillem Cazassus
Title: Extending down Donaldson-Floer theory
Abstract: The Donaldson polynomials are powerful invariants in Low Dimensional Topology: they are able to distinguish exotic smooth 4-manifolds. They are rooted in theoretical physics (Yang-Mills Gauge Theory) and are difficult to compute, as they involve solving a PDE (the Anti-Self-Dual equation). Their 3D counterpart, Instanton Floer homology groups, are equally important invariants for 3-manifolds or links.
I will report on a program aimed at computing these by "cut-and-paste" operations. Specifically I will explain how to construct an "extended Topological Field Theory" that should recover them. This will involve going from Gauge Theory to Symplectic Geometry, Hamiltonian actions and some new Homotopical Algebra.
This will be based on arXiv:1903.10686, arXiv:2404.17393 and some work in progress with A. Hock and T. Mazuir to appear soon.

Speaker: Noémie Legout
Title: Calabi-Yau structures on the Chekanov-Eliashberg algebra of Legendrians
Abstract: We prove that the Chekanov-Eliashberg algebra (CE-algebra) admits an absolute Calabi-Yau structure in the case the Legendrian is a displaceable sphere. It means that there is a quasi-isomorphism between the CE-algebra seen as a bimodule over itself, and the inverse dualizing bimodule. We give a geometric interpretation of this quasi-isomorphism in terms of the Rabinowitz complex associated to a Legendrian. In a work in progress with Georgios Dimitroglou-Rizell, we consider Legendrians which are not necessarily spheres. In this case, the CE-algebra is endowed with a relative Calabi-Yau structure.

Speaker: Adrian Petr
Title: Fukaya category over the Novikov ring and wrapped Floer theory.
Abstract: Let W be a Liouville manifold whose boundary at infinity is the total space of a prequantization bundle p over a symplectic manifold B. Given a cylindrical exact Lagrangian L in W, the restriction i of p to the boundary at infinity of L is a Lagrangian immersion in B. Assuming that W is topologically simple and B is monotone with minimal Chern number different from 1, we relate the Fukaya category of i over the Novikov ring and the wrapped Floer theory of L.

Speaker: Johan Rydholm
Title: Geometric realization of type \tilde{A}_n preprojective algebras and homological mirror symmetry
Abstract: I will talk about geometric realizations of different versions of type \tilde{A}_n preprojective algebras, arising in homological mirror symmetry statements relating the algebraic resolutions of singularities and the Milnor fibres corresponding to the cyclic groups, in complex dimension 2. This includes computations on the A-side of both manifolds.

Speaker: Matthias Scharitzer
Title: Skein-valued cluster transformation from Legendrian mutation.
Abstract: In their series of works Ekholm and Shende defined a new invariant for certain classes of 3-dimensional (non-exact) Lagrangian cobordisms: They count curves by the knot that they trace out in the Lagrangian. Similar to an augmentation, a Lagragian cobordism induces a relation between certain (skein-valued) curve counts with tangencies at infinity. In recent work with Vivek Shende, we considered cobordisms which relate two Legendrians differing by a local operation called Legendrian mutation. We identified some cases in which the induced algebraic operation is a so-called skein-valued cluster transformation. In this talk, I will report on our recent work, possible future directions and, if time permits, applications.

Speaker: Maksim Stokić
Title: $C^0$ contact and symplectic geometry of smooth submanifolds.
Abstract: The celebrated Eliashberg-Gromov rigidity theorem allows for the definition of symplectic and contact homeomorphisms as $C^0$ limits of symplectic (resp. contact) diffeomorphisms. In this talk, we will provide an overview of the $C^0$ flexibility and rigidity properties of smooth submanifolds, with a particular emphasis on the flexibility of isotropic submanifolds. Special attention will be given to the case of Legendrian submanifolds.

Speaker: Alex Takeda
Title: Properadic formality of Poincaré duality structures
Abstract: Questions about the formality of an algebra over a given dg operad can often be resolved by calculating a certain obstruction class associated to it, known as the Kaledin class. Automatic vanishing of this class implies, for example, the formality of the algebra of cochains on spheres and other highly connected spaces. In this talk I will describe how an extension of this definition for properadic algebras allows us to address formality questions not only of space in its own, but of (possibly noncommutative) spaces endowed with a certain type of Poincaré duality structure, namely a pre-Calabi-Yau structure. Using a formalism relating open and closed 2d topological field theories, this also implies formality of the framed E2-algebra associated to the space in question. This is joint work with Coline Emprin.

Speaker: Bingyu Zhang
Title: Hochschild cohomology of Tamarkin category and filtered symplectic (co)homology.
Abstract: We can define a Tamarkin category for an open set in a cotangent bundle using the microlocal geometry of sheaves, which is naturally filtered. In this talk, I will explain how to relate Hochschild cohomology of Tamarkin category (natually filtered) and the filtered symplectic (co)homology. The talk is based on a joint work with Christopher Kuo and Vivek Shende.