Departement Mathematik

Symplectic geometry seminar

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Herbstsemester 2016

Datum / Zeit Referent:in Titel Ort
29. August 2016
15:15-16:30 		Dr. Agnès Gadbled
Univ. Porto and Univ. Grenoble
Details

Symplectic Geometry Seminar

Titel Toric constructions of monotone Lagrangian submanifolds in CP² and CP¹xCP¹
Referent:in, Affiliation Dr. Agnès Gadbled, Univ. Porto and Univ. Grenoble
Datum, Zeit 29. August 2016, 15:15-16:30
Ort HG G 43
Abstract In a previous paper, I proved that two very different constructions of monotone Lagrangian tori are Hamiltonian isotopic inside $\mathbb{CP}^2$ by comparing both of them to a third one called modified Chekanov torus. This modified Chekanov torus has an interesting projection under the standard moment map of $\mathbb{CP}^2$ and motivates a method of construction of (monotone) Lagrangian submanifolds in symplectic toric manifolds. I will explain how this method gives some old and new monotone examples in $\mathbb{CP}^2$ and $\mathbb{CP}^1 \times \mathbb{CP}^1$. This is joint work with Miguel Abreu (IST, Lisbon).
Toric constructions of monotone Lagrangian submanifolds in CP² and CP¹xCP¹read_more
HG G 43
19. September 2016
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 19. September 2016, 15:15-16:30
Ort HG G 43
No seminar
HG G 43
26. September 2016
15:15-16:30 		Paul Biran
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Metric Aspects of Lagrangian Cobordism
Referent:in, Affiliation Paul Biran, ETH Zürich
Datum, Zeit 26. September 2016, 15:15-16:30
Ort HG G 43
Metric Aspects of Lagrangian Cobordism
HG G 43
3. Oktober 2016
15:15-16:30 		Guan Huang
University of Maryland
Details

Symplectic Geometry Seminar

Titel Marked length spectrum of a generic convex planar domain determines eigenvalues of "maximal" periodic orbits
Referent:in, Affiliation Guan Huang, University of Maryland
Datum, Zeit 3. Oktober 2016, 15:15-16:30
Ort HG G 43
Abstract The famous questions of M. Kac ``Can you hear the shape of a drum?'' in mathematical terms asks if the Laplace spectrum determines a domain. The question is open for convex domains with smooth boundaries. To each such a domain one can associate the length spectrum consisting of periods of all billiard periodic orbits. It turns out the length spectrum is a symplectic invariant of the underlying billiard symplectic structure. Generically the Laplace spectrum determines the length one. During the talk we show that for a generic strictly convex planar domain a ``maximal'' part of the length specturm determines eigenvalues of the linearization of ``maximal'' (Aubry-Mather) periodic orbits. This is closely related to a question posed in the 80s by Guillemin-Melrose. This is a jointed work with V. Kaloshin and A. Sorrentino.
Marked length spectrum of a generic convex planar domain determines eigenvalues of "maximal" periodic orbitsread_more
HG G 43
10. Oktober 2016
15:15-16:30 		Mads Bisgaard
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Measuring Lagrangian cobordisms using spectral numbers
Referent:in, Affiliation Mads Bisgaard, ETH Zürich
Datum, Zeit 10. Oktober 2016, 15:15-16:30
Ort HG G 43
Measuring Lagrangian cobordisms using spectral numbers
HG G 43
17. Oktober 2016
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 17. Oktober 2016, 15:15-16:30
Ort HG G 43
No seminar
HG G 43
24. Oktober 2016
15:15-16:30 		Vadim Kaloshin
University of Maryland & ITS-ETH Zürich
Details

Symplectic Geometry Seminar

Titel On Deformational Spectral Rigidity of Convex Symmetric Planar Domains
Referent:in, Affiliation Vadim Kaloshin, University of Maryland & ITS-ETH Zürich
Datum, Zeit 24. Oktober 2016, 15:15-16:30
Ort HG G 43
Abstract One can associate to a planar convex domain Ω ⊂ R2 two types of spectra: the Laplace spectrum consisting of eigenvalues of a Dirichlet problem and the length spectrum consisting of perimeters of all periodic orbits of a billiard problem inside Ω. The Laplace and length spectra are closely related, generically the first determines the second. M. Kac asked if the Laplace spectrum determines a domain Ω. There are counterexamples. During the talk we show that a planar axis symmetric domain close to the circle cant be smoothly deformed preserving the length spectrum unless the deformation is a rigid motion. This gives a partial answer to a question of P. Sarnak. This is a joint work with J. De Simoi and Q. Wei.
On Deformational Spectral Rigidity of Convex Symmetric Planar Domainsread_more
HG G 43
31. Oktober 2016
15:15-16:30 		Kathrin Näf
ETH Zürich
Details

Symplectic Geometry Seminar

Titel On the existence of translated points
Referent:in, Affiliation Kathrin Näf, ETH Zürich
Datum, Zeit 31. Oktober 2016, 15:15-16:30
Ort HG G 43
On the existence of translated points
HG G 43
7. November 2016
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 7. November 2016, 15:15-16:30
Ort HG G 43
No seminar
HG G 43
14. November 2016
15:15-16:30 		Urs Frauenfelder
Universityät Augsburg
Details

Symplectic Geometry Seminar

Titel Periodic orbits in the restricted three body problem and Arnold's J^+ invariant
Referent:in, Affiliation Urs Frauenfelder, Universityät Augsburg
Datum, Zeit 14. November 2016, 15:15-16:30
Ort HG G 43
Abstract This is joint work with Kai Cieliebak. After regularization periodic orbits in the restricted three body problem become knots in RP^3. Their projection to position space is a curve in the plane. We show that Arnold's J^+ invariant is invariant under homotopies of periodic orbits and gives an additional invariant to their knot type in RP^3.
Periodic orbits in the restricted three body problem and Arnold's J^+ invariantread_more
HG G 43
21. November 2016
15:15-16:30 		Luis Haug
ETH Zürich
Details

Symplectic Geometry Seminar

Titel Constructing Lagrangian cobordisms by antisurgery
Referent:in, Affiliation Luis Haug, ETH Zürich
Datum, Zeit 21. November 2016, 15:15-16:30
Ort HG G 43
Constructing Lagrangian cobordisms by antisurgery
HG G 43
28. November 2016
15:15-16:30 		Michael Hutchings
Berkeley University
Details

Symplectic Geometry Seminar

Titel Infinitely many Reeb orbits for many contact three-manifolds
Referent:in, Affiliation Michael Hutchings, Berkeley University
Datum, Zeit 28. November 2016, 15:15-16:30
Ort HG G 43
Infinitely many Reeb orbits for many contact three-manifolds
HG G 43
5. Dezember 2016
15:15-16:30 		Emmy Murphy
MIT / Northwestern University
Details

Symplectic Geometry Seminar

Titel The Legendrian DGA of a cubic planar graph
Referent:in, Affiliation Emmy Murphy, MIT / Northwestern University
Datum, Zeit 5. Dezember 2016, 15:15-16:30
Ort HG G 43
Abstract Associated to any planar cubic graph, we have a Legendrian surface in S*R^3, as defined by Treumann and Zaslow. We discuss how to compute the contact homology DGA of this Legendrian. It is clear that sheaves on this Legendrian recover the chromatic data of the graph, so by following the expected equivalence of augmentations and sheaves, we obtain a new definition of an n-coloring of a planar graph, interesting in part because the definition is much more nonlinear compared to other known definitions. We also discuss combinatorial moves which correspond to cobordisms, fillings, and connect sums, relationships with loose Legendrians.
The Legendrian DGA of a cubic planar graphread_more
HG G 43

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