Departement Mathematik

Symplectic geometry seminar

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Frühjahrssemester 2023

Datum / Zeit Referent:in Titel Ort
6. März 2023
15:15-16:30 		Frank Kutzschebauch
Universität Bern
Details

Symplectic Geometry Seminar

Titel The density property for complex manifolds
Referent:in, Affiliation Frank Kutzschebauch, Universität Bern
Datum, Zeit 6. März 2023, 15:15-16:30
Ort HG G 43
Abstract Most complex manifolds have a trivial group of holomorphic symmetries. To the contrary $\Cn$ for $n\ge 2$ has a huge automorphism group which was studied a lot by Rudin and Rosay in the late 1980’s. Answering a question by Rudin, Andersen and Lempert proved that a certain infinite dimensional subgroup of automorphisms is dense, however meagre, in the holomorphic automorphism group. Their result was improved by Forstneric and Rosay to show that any local phase flow of a time dependend holomorphic vector field can be approximated on compacta by a family of holomorphic automorphisms. This remarkable result let to an enormous number of applications for complex geometry. In 2002 Varolin generalized this to complex manifolds calling it density property and gave first examples of such highly symmetric objects. Kaliman and the speaker developed effective tools for proving the density property. The list of such manifolds is rather long nowadays and is growing steadily. The geometric applications of the density property are as well becoming more and more. We try to give an overview of this area of research also called Andersen-Lempert theory. There is a version of volume density property. Natural generalizations to symplectic holomorphic manifolds are awaiting us in the future.
The density property for complex manifoldsread_more
HG G 43
13. März 2023
15:15-16:30 		Huang Gaofeng
Universität Bern
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Symplectic Geometry Seminar

Titel Symplectic Density Property for Calogero—Moser Spaces
Referent:in, Affiliation Huang Gaofeng, Universität Bern
Datum, Zeit 13. März 2023, 15:15-16:30
Ort HG G 43
Abstract In contrast to density property or volume density property, there are few symplectic Stein manifolds known to admit symplectic holomorphic density property. One example is $\mathbb{C}^{2n}$. In this talk we first introduce the symplectic holomorphic density property with the corresponding version of Anders{\'e}n--Lempert theory. Then we outline a proof for this property for the Calogero--Moser space $\mathcal{C}_n$ of $n$ particles, and describe its group of holomorphic symplectic automorphisms. This is joint work with Rafael B. Andrist.
Symplectic Density Property for Calogero—Moser Spacesread_more
HG G 43
20. März 2023
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 20. März 2023, 15:15-16:30
Ort
No seminar
27. März 2023
15:15-16:30 		Yusuke Kawamoto
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Isolated hypersurface singularities, spectral invariants, and quantum cohomology
Referent:in, Affiliation Yusuke Kawamoto, ETH Zürich
Datum, Zeit 27. März 2023, 15:15-16:30
Ort HG G 43
Abstract We discuss the relation between hypersurface singularities (e.g. ADE, $\widetilde{E}_{6},\widetilde{E}_{7},\widetilde{E}_{8}$, etc) and spectral invariants, which are symplectic invariants coming from Floer theory.
Isolated hypersurface singularities, spectral invariants, and quantum cohomologyread_more
HG G 43
3. April 2023
15:15-16:30 		Patricia Dietzsch
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Lagrangian Hofer metric and barcodes
Referent:in, Affiliation Patricia Dietzsch, ETH Zürich
Datum, Zeit 3. April 2023, 15:15-16:30
Ort HG G 43
Abstract Filtered Lagrangian Floer homology gives rise to a barcode associated to a pair of Lagrangians. It is well-known that the lengths of the finite bars and the spectral distance are lower bounds of the Lagrangian Hofer metric. In this talk we will discuss a reverse inequality: We will show an upper bound of the Lagrangian Hofer distance between equators in the cylinder in terms of a weighted sum of the lengths of the finite bars and the spectral distance.
Lagrangian Hofer metric and barcodesread_more
HG G 43
10. April 2023
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 10. April 2023, 15:15-16:30
Ort
No seminar
24. April 2023
15:15-16:30 		Reto Kaufmann
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Symplectic Toric Submanifolds and Faces of the Moment Polytope
Referent:in, Affiliation Reto Kaufmann, ETH Zürich
Datum, Zeit 24. April 2023, 15:15-16:30
Ort HG G 43
Abstract By Delzant's Theorem, symplectic toric manifolds are classified by their unimodular moment polytopes. In this talk, we will discuss the bijection between the faces of the moment polytope and the symplectic toric submanifolds of the corresponding symplectic toric manifold. To study recursive aspects like this, it is useful to generalise the notion of a symplectic toric manifold. First we present how this generalisation works in the local picture, given by symplectic toric representations and unimodular polyhedral cones. Then, we will show how this can be used to establish the global correspondence between submanifolds and faces.
Symplectic Toric Submanifolds and Faces of the Moment Polytoperead_more
HG G 43
1. Mai 2023
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 1. Mai 2023, 15:15-16:30
Ort
No seminar
8. Mai 2023
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 8. Mai 2023, 15:15-16:30
Ort
No seminar
15. Mai 2023
15:15-16:30 		Sara Kalisnik
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Parametrized Homology & Sensor Networks
Referent:in, Affiliation Sara Kalisnik, ETH Zürich
Datum, Zeit 15. Mai 2023, 15:15-16:30
Ort HG G 43
Abstract An important problem with sensor networks is that they do not provide information about the regions that are not covered by their sensors. If the sensors in a network are static, then the Alexander Duality Theorem from classic algebraic topology is sufficient to determine the coverage of a network. However, in many networks the sensors change position with time. In the case of dynamic sensor networks, one considers the covered and uncovered regions as parametrized spaces with respect to time. In this talk, I will define parametrized homology, a variant of zigzag persistent homology that measures how the homology of the level sets of the space changes as we vary the parameter. I will also present a version of the Alexander Duality Theorem in the setting of parametrized homology. This approach sheds light on the practical problem of loss of coverage within dynamic sensor networks.
Parametrized Homology & Sensor Networksread_more
HG G 43
22. Mai 2023
15:15-16:30 		Miguel Abreu
Instituto Superior Tecnico Lisbon
Details

Symplectic Geometry Seminar

Titel Contact invariants of Q-Gorenstein toric contact manifolds and the Ehrhart (quasi-)polynomials of their toric diagrams
Referent:in, Affiliation Miguel Abreu, Instituto Superior Tecnico Lisbon
Datum, Zeit 22. Mai 2023, 15:15-16:30
Ort HG G 43
Abstract Q-Gorenstein toric contact manifolds provide an interesting class of contact manifolds with torsion first Chern class. They are completely determined by certain rational convex polytopes, called toric diagrams. The main goal of this talk is to describe how the cylindrical contact homology invariants of a Q-Gorenstein toric contact manifold are related to the Ehrhart (quasi-)polynomial of its toric diagram. This is part of joint work with L. Macarini and M. Moreira, arXiv:2202.00442. If time permits, I will also briefly discuss an application to the study of periodic Reeb orbits on lens spaces (part of joint work with L. Macarini and H. Liu, arXiv:2211.16470).
Contact invariants of Q-Gorenstein toric contact manifolds and the Ehrhart (quasi-)polynomials of their toric diagramsread_more
HG G 43
29. Mai 2023
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 29. Mai 2023, 15:15-16:30
Ort
No seminar

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