Departement Mathematik

Symplectic geometry seminar

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Frühjahrssemester 2018

Datum / Zeit Referent:in Titel Ort
26. Februar 2018
15:15-16:30 		Prof. Dr. Peter Albers
Universität Heidelberg
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Symplectic Geometry Seminar

Titel Symplectic billiards
Referent:in, Affiliation Prof. Dr. Peter Albers, Universität Heidelberg
Datum, Zeit 26. Februar 2018, 15:15-16:30
Ort HG G 43
Symplectic billiards
HG G 43
5. März 2018
15:15-16:30 		Dietmar Salamon
ETH Zürich
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Symplectic Geometry Seminar

Titel Diffeomorphism groups, moment maps, and the Ricci form
Referent:in, Affiliation Dietmar Salamon, ETH Zürich
Datum, Zeit 5. März 2018, 15:15-16:30
Ort HG G 43
Abstract This talk is about joint work with Oscar Garcia-Prada and Samuel Trautwein. We prove that the Ricci form is a moment map for the action of the group of exact volume preserving diffeomorphisms on the space of almost complex structures. This observation gives rise to an extended nonKähler Weil--Petersson symplectic form on the Teichmüller space of isotopy classes of complex structures with real first Chern class zero and nonempty Kähler cone.
Diffeomorphism groups, moment maps, and the Ricci formread_more
HG G 43
12. März 2018
15:15-16:30 		Charel Antony
ETH Zurich
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Symplectic Geometry Seminar

Titel Vanishing cycles near A2 singularities
Referent:in, Affiliation Charel Antony, ETH Zurich
Datum, Zeit 12. März 2018, 15:15-16:30
Ort HG G 43
Vanishing cycles near A2 singularities
HG G 43
19. März 2018
15:15-16:30 		Dr. Jagna Wisniewska
ETH Zurich, Switzerland
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Symplectic Geometry Seminar

Titel Rabinowitz Floer Homology for Tentacular Hamiltonians
Referent:in, Affiliation Dr. Jagna Wisniewska, ETH Zurich, Switzerland
Datum, Zeit 19. März 2018, 15:15-16:30
Ort HG G 43
Rabinowitz Floer Homology for Tentacular Hamiltonians
HG G 43
26. März 2018
15:15-16:30
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Symplectic Geometry Seminar

Titel no seminar
Referent:in, Affiliation
Datum, Zeit 26. März 2018, 15:15-16:30
Ort
no seminar
23. April 2018
15:15-16:30 		Mads Bisgaard
ETH Zürich
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Symplectic Geometry Seminar

Titel Symplectic Mather theory
Referent:in, Affiliation Mads Bisgaard, ETH Zürich
Datum, Zeit 23. April 2018, 15:15-16:30
Ort HG G 43
Abstract I will discuss two different approaches to systematically studying invariant sets of Hamiltonian systems. The first approach builds heavily on Viterbo's symplectic homogenization procedure. I will discuss how an analogue of Mather's alpha-function arises from homogenized Floer homological Lagrangian spectral invariants and how it gives rise to the existence of an analogue of Mather measures (from Aubry-Mather theory) to general symplectic manifolds. Unlike what happens in the Tonelli case, I will show that the support of these measures can be extremely "wild" in the non-convex case. I will explain how this phenomenon is closely related to diffusion phenomena such as Arnold' diffusion. The second approach builds on work due to Buhovsky-Entov-Polterovich and provides a C^0-analogue of Mather measures for Hamiltonians on "flexible" symplectic manifolds. I will discuss applications to Hamiltonian systems on twisted cotangent bundles and R^2n.
Symplectic Mather theoryread_more
HG G 43
30. April 2018
15:15-16:30 		Dr. Gabriele Benedetti
Universität Leipzig
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Symplectic Geometry Seminar

Titel A local systolic inequality in contact and symplectic geometry
Referent:in, Affiliation Dr. Gabriele Benedetti, Universität Leipzig
Datum, Zeit 30. April 2018, 15:15-16:30
Ort HG G 43
Abstract In this talk, which reports on a joint work with Jungsoo Kang, we formulate a local systolic inequality for Reeb flows and Hamiltonian diffeomorphisms, which we establish in low dimension. As a consequence, we derive bounds for the minimal action of periodic orbits of certain magnetic flows on orientable closed surfaces. If time permits, we will also show how Reeb and Hamiltonian systolic inequalities are particular cases of a more general inequality in the wider class of odd-symplectic forms.
A local systolic inequality in contact and symplectic geometryread_more
HG G 43
7. Mai 2018
15:15-16:30 		Martin Guest
Waseda University, Tokyo, Japan
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Symplectic Geometry Seminar

Titel The Coxeter Plane and the tt*-Toda equations
Referent:in, Affiliation Martin Guest, Waseda University, Tokyo, Japan
Datum, Zeit 7. Mai 2018, 15:15-16:30
Ort HG G 43
Abstract The 2D topological-antitopological fusion equations were introduced by Cecotti and Vafa in the 1990's. They are a system of "integrable" nonlinear pde with rich connections to geometry, e.g. Frobenius manifolds and quantum cohomology, but they are difficult to solve (and the same applies - evenmore so - to the more recently studied 4D tt* equations). I will discuss a special case of the 2D tt* equations, the tt*-Toda equations, where computations are feasible. Already here, interesting links with more classical topics arise - for example the Coxeter Plane.
The Coxeter Plane and the tt*-Toda equationsread_more
HG G 43
14. Mai 2018
15:15-16:15 		Dr. Gleb Smirnov
SISSA, Trieste
Details

Symplectic Geometry Seminar

Titel Symplectomorphism groups of elliptic ruled surfaces
Referent:in, Affiliation Dr. Gleb Smirnov, SISSA, Trieste
Datum, Zeit 14. Mai 2018, 15:15-16:15
Ort HG G 43
Abstract An elliptic ruled surface is a 4-manifold satisfying the condition that it has a holomorphic fibration over an elliptic curve with fibers that are projective lines. Every elliptic ruled surface is algebraic, and, in particular, a Kaehler surface. In this talk I would like to discuss the rational homotopy type of the symplectomorphism group of elliptic ruled surfaces when the Kaehler form satisfies the following constraint: there are no symplectic 2-submanifolds of negative self-intersection index. More precisely, we will show that the symplectomorphism group is rationally homotopy equivalent to the 2-dimensional torus.
Symplectomorphism groups of elliptic ruled surfacesread_more
HG G 43
* 1. Juni 2018
11:15-12:15 		Yael Karshon
University of Toronto, Canada
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Symplectic Geometry Seminar

Titel Non-linear Maslov index on lens spaces
Referent:in, Affiliation Yael Karshon, University of Toronto, Canada
Datum, Zeit 1. Juni 2018, 11:15-12:15
Ort HG G 19.1
Abstract Let L be a lens space with its standard contact structure. We construct a "non-linear Maslov index", which associates an integer to any contact isotopy of L, and which gives a quasimorphism on the universal cover of the identity component of the contactomorphism group of L. We use it to prove contact rigidity properties of L. This work is joint with Gustavo Granja, Milena Pabinia, and Sheila (Margherita) Sandon, and it follows earlier work of Givental and Theret that applied to real and complex projective spaces.
Non-linear Maslov index on lens spacesread_more
HG G 19.1

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