Departement Mathematik

Symplectic geometry seminar

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Herbstsemester 2019

Datum / Zeit Referent:in Titel Ort
16. September 2019
15:15-16:30 		Jeff Hicks
Cambridge University
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Symplectic Geometry Seminar

Titel Counting holomorphic disks on Lagrangian Cobordisms
Referent:in, Affiliation Jeff Hicks, Cambridge University
Datum, Zeit 16. September 2019, 15:15-16:30
Ort HG G 43
Abstract The count of holomorphic disks with boundary on a Lagrangian submanifold can be used to construct invariants of Lagrangian submanifolds; at the same time, their presence can be an obstruction to using tools like Lagrangian intersection Floer theory. One such obstruction appears in the theory of Lagrangian cobordisms, where a general principle of Biran and Cornea tells us that two cobordant Lagrangians should have matching Floer theoretic information --- provided that the Lagrangian cobordism does not bound holomorphic disks. We will look at a few examples of where this condition can be weakened, and what the presence of holomorphic disks with boundary on a Lagrangian cobordism means for the Floer theory of its ends.
Counting holomorphic disks on Lagrangian Cobordismsread_more
HG G 43
23. September 2019
15:15-16:30
Details

Symplectic Geometry Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 23. September 2019, 15:15-16:30
Ort HG G 43
no seminar
HG G 43
30. September 2019
15:15-16:30
Details

Symplectic Geometry Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 30. September 2019, 15:15-16:30
Ort HG G 43
no seminar
HG G 43
7. Oktober 2019
15:15-16:30 		Baptiste Chantraine
University of Nantes
Details

Symplectic Geometry Seminar

Titel Generation of the wrapped Fukaya category of a Weinstein sector
Referent:in, Affiliation Baptiste Chantraine, University of Nantes
Datum, Zeit 7. Oktober 2019, 15:15-16:30
Ort HG G 43
Abstract A Weinstein manifold W is an exact symplectic manifold such that the dual of a primitive of the symplectic form is gradient like for some function. This leads to a particular handle decomposition of the manifolds out of which natural Lagrangian submanifolds appear: the cocores of the critical handles. Those cocores are objects in the so-called wrapped Fukaya category of W. It turns out that all other objects of this category can be expressed as iterated cone built out of those. After introducing the necessary notions to understand it I will explain how this algebraic statement follows from some geometric considerations and some properties of a Floer complexes associated to Lagrangian cobordisms between Legendrian submanifolds. This is joint work with G. Dimitroglou-Rizell, P. Ghiggin and R. Golovko.
Generation of the wrapped Fukaya category of a Weinstein sectorread_more
HG G 43
14. Oktober 2019
15:15-16:30 		Fabian Ziltener
University of Utrecht
Details

Symplectic Geometry Seminar

Titel Coisotropic submanifolds of symplectic manifolds, leafwise fixed points, and spherical nonsqueezing
Referent:in, Affiliation Fabian Ziltener, University of Utrecht
Datum, Zeit 14. Oktober 2019, 15:15-16:30
Ort HG G 43
Abstract My talk is partly about joint work with Dusan Joksimovic, and with Jan Swoboda. Consider a symplectic manifold $(M,\omega)$, a closed coisotropic submanifold $N$ of $M$, and a Hamiltonian diffeomorphism $\phi$ on $M$. A leafwise fixed point for $\phi$ is a point $x\in N$ that under $\phi$ is mapped to its isotropic leaf. These points generalize fixed points and Lagrangian intersection points. In classical mechanics leafwise fixed points correspond to trajectories that are changed only by a time-shift, when an autonomous mechanical system is perturbed in a time-dependent way. J. Moser posed the following problem: Find conditions under which leafwise fixed points exist. A special case of this problem is V.I. Arnold's conjecture about fixed points of Hamiltonian diffeomorphisms. The main result presented in this talk is that leafwise fixed points exist if the Hamiltonian diffeomorphism is the time-1-map of a Hamiltonian flow whose restriction to $N$ stays $C^0$-close to the inclusion $N\to M$. I will also mention a version of this result that is locally uniform in the symplectic form and the coisotropic submanifold. As an application of a related result, no neighbourhood of the unit sphere symplectically embeds into the unit symplectic cylinder. This sharpens Gromov's nonsqueezing result.
Coisotropic submanifolds of symplectic manifolds, leafwise fixed points, and spherical nonsqueezingread_more
HG G 43
21. Oktober 2019
15:15-16:30 		Dr. Lucas Dahinden
Universität Heidelberg
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Symplectic Geometry Seminar

Titel Volume growth of positive contactomorphisms
Referent:in, Affiliation Dr. Lucas Dahinden, Universität Heidelberg
Datum, Zeit 21. Oktober 2019, 15:15-16:30
Ort HG G 43
Abstract In cooriented contact manifolds there is a natural notion of moving positively, which gives birth to the notion of positive contactomorphism. The quest of studying the dynamical behaviour of these maps includes counting chords between special (Legendrian) submanifolds, which has implications for volume growth and topological entropy. The machinery we use is symplectic homology and Rabinowitz--Floer homology. In this talk I will try to avoid the heavy part of the machinery. Instead I focus on encoding geometric data in such an action functional, and on how to extract dynamical information.
Volume growth of positive contactomorphismsread_more
HG G 43
28. Oktober 2019
15:15-16:30 		Yanki Lekili
King's college, London
Details

Symplectic Geometry Seminar

Titel A symplectic look at the Fargues-Fontaine curve
Referent:in, Affiliation Yanki Lekili, King's college, London
Datum, Zeit 28. Oktober 2019, 15:15-16:30
Ort HG G 43
Abstract I will explain how to introduce a Frobenius twist in the construction of Fukaya category by equipping the underlying symplectic manifold with a locally constant sheaf of rings. When the fiber of this sheaf of rings is perfectoid of characteristic p, it is possible to specialize the Novikov parameter t = 1, and the Lagrangians in the resulting category can be matched with vector bundles on the equal-characteristic-version of the Fargues-Fontaine curve. Don't worry, it is just a story about triangles on a torus. Joint work with David Treumann.
A symplectic look at the Fargues-Fontaine curveread_more
HG G 43
4. November 2019
15:15-16:15 		Agnès Gadbled
Uppsala University
Details

Symplectic Geometry Seminar

Titel Categorical action of the braid group of the cylinder: symplectic aspect
Referent:in, Affiliation Agnès Gadbled, Uppsala University
Datum, Zeit 4. November 2019, 15:15-16:15
Ort HG G 43
Abstract Khovanov and Seidel gave in 2000 an action of the classical braid group on a category of algebraic nature that categorifies the Burau representation. They proved the faithfulness of this action through the study of curves in a punctured disk (while Burau representation is not faithful for braids with five strands or more). In a recent article with Anne-Laure Thiel and Emmanuel Wagner, we extended this result to the braid group of the cylinder. The work of Khovanov and Seidel also had a symplectic aspect that we now generalize. In this talk, I will explain the strategy and tools to get a symplectic monodromy in our case and prove its injectivity. If time permits, I will explain how this action lifts to a symplectic categorical representation on a Fukaya category that should be related to the algebraic categorical representation. This is a joint work in progress with Anne-Laure Thiel and Emmanuel Wagner.
Categorical action of the braid group of the cylinder: symplectic aspectread_more
HG G 43
11. November 2019
15:15-16:30
Details

Symplectic Geometry Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 11. November 2019, 15:15-16:30
Ort HG G 43
no seminar
HG G 43
18. November 2019
15:15-16:30
Details

Symplectic Geometry Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 18. November 2019, 15:15-16:30
Ort HG G 43
no seminar
HG G 43
25. November 2019
15:15-16:30 		Sara Tukachinsky
Institute for Advanced Study, USA
Details

Symplectic Geometry Seminar

Titel Counts of pseudoholomorphic curves: Definition, calculations, and more
Referent:in, Affiliation Sara Tukachinsky, Institute for Advanced Study, USA
Datum, Zeit 25. November 2019, 15:15-16:30
Ort HG G 43
Abstract Genus zero open Gromov-Witten (OGW) invariants should count pseudoholomorphic disks in a symplectic manifold with boundary conditions in a Lagrangian submanifold, satisfying various constraints at boundary and interior marked points. In a joint work with Jake Solomon we developed an approach for defining OGW invariants using machinery from Fukaya A_\infty algebras. In a recent work, also joint with Solomon, we find that the generating function of OGW satisfies a system of PDE called open WDVV equations. This PDE translates to an associativity relation for a quantum product on the relative cohomology. For projective spaces, open WDVV give rise to recursions that, together with other properties, allow the computation of all OGW invariants.
Counts of pseudoholomorphic curves: Definition, calculations, and moreread_more
HG G 43
2. Dezember 2019
15:15-16:30 		Emmanuel Opshtein
Université de Strasbourg
Details

Symplectic Geometry Seminar

Titel Squeezing Lagrangian tori in R^4
Referent:in, Affiliation Emmanuel Opshtein, Université de Strasbourg
Datum, Zeit 2. Dezember 2019, 15:15-16:30
Ort HG G 43
Abstract A long-standing problem, known as the Lagrangian recurrence conjecture concerns the problem of knowing how many different Hamiltonian copies of a Lagrangian torus can be found in some manifold. A particular, well-studied case of this question is the problem of non-displaceability. With Richard Hind, we studied another side of this question : how much can a given Lagrangian torus be squeezed ? We find a complete answer for product tori in R^4, which shows an interesting mixture of rigidity and flexibility : L(1,x) is fully rigid for 12 however, most the rigidity disappears and the only remaining constraint is that L(1,x) cannot be squeezed in a ball smaller than 3.
Squeezing Lagrangian tori in R^4read_more
HG G 43
* 9. Dezember 2019
13:15-14:15 		Bahar Acu
Northwestern University
Details

Symplectic Geometry Seminar

Titel Planarity in higher-dimensional contact manifolds
Referent:in, Affiliation Bahar Acu, Northwestern University
Datum, Zeit 9. Dezember 2019, 13:15-14:15
Ort HG G 19.2
Abstract Planar contact manifolds, those that correspond to an open book decomposition with genus zero pages, have been intensively studied to understand several aspects of 3-dimensional contact topology. In this talk, we define "iterated planar contact manifolds", a higher-dimensional analog of planar contact manifolds, by using topological tools such as open book decompositions and Lefschetz fibrations. We provide history on some of the existing low-dimensional results regarding Reeb dynamics and symplectic fillings of planar contact manifolds, and explain some generalization of those results to higher dimensions via iterated planar structure.
Planarity in higher-dimensional contact manifoldsread_more
HG G 19.2

Hinweise: mit einem Stern gekennzeichnete Ereignisse (*) zeigen an, dass die Zeit und/oder der Ort von der üblichen Zeit und/oder dem üblichen Ort abweichen und wenn Sie möchten, können Sie den iCal/ics-Kalender abonnieren.

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