Symplectic geometry seminar

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Spring Semester 2012

Date / Time Speaker Title Location
8 February 2012
15:15-16:30
Prof. Dr. Johannes Walcher
McGill University, Canada
Event Details

Symplectic Geometry Seminar

Title Arithmetic of normal functions and mirror symmetry
Speaker, Affiliation Prof. Dr. Johannes Walcher, McGill University, Canada
Date, Time 8 February 2012, 15:15-16:30
Location HG G 43
Abstract Hodge theory, via mirror symmetry, has been making enumerative predictions about Gromov-Witten theory of Calabi-Yau threefolds. In particular, normal functions attached to algebraic cycles contain information about "numbers" of holomorphic discs ending on Lagrangian submanifolds. The most recent calculations concern algebraic cycles defined over finite extensions of the rational numbers. Still, there is convincing evidence (and a fair number of excuses) that the resulting invariants must admit an enumerative interpretation on the symplectic side. This interpretation will involve a new, arithmetic, twist of the di-logarithm: The D-logarithm.
Arithmetic of normal functions and mirror symmetryread_more
HG G 43
20 February 2012
15:15-16:30
Georgios Rizell
Uppsala University, Sweden
Event Details

Symplectic Geometry Seminar

Title Knotted Legendrian surfaces with few Reeb chords
Speaker, Affiliation Georgios Rizell, Uppsala University, Sweden
Date, Time 20 February 2012, 15:15-16:30
Location HG G 43
Abstract For g > 0, we construct g + 1 Legendrian embeddings of a surface of genus g into standard contact R^5 which lie in pairwise distinct Legendrian isotopy classes and which all have g + 1 transverse Reeb chords (g + 1 is the minimal number of chords for Legendrian surfaces which admit a linearization of its Legendrian contact homology). We investigate these surfaces from the point-of-view of Legendrian contact homology as well as generating families. Gradient flow trees are used for computing the differentials.
Knotted Legendrian surfaces with few Reeb chordsread_more
HG G 43
27 February 2012
15:15-16:30
Paolo Rossi
University of Zurich
Event Details

Symplectic Geometry Seminar

Title Non equivariant contact homology revisited: a Poisson-Nijenhuis structure in SFT
Speaker, Affiliation Paolo Rossi, University of Zurich
Date, Time 27 February 2012, 15:15-16:30
Location HG G 43
Non equivariant contact homology revisited: a Poisson-Nijenhuis structure in SFT
HG G 43
19 March 2012
15:15-16:15
Jonathan Evans
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Pseudoholomorphic curves and nilpotent Lie algebras
Speaker, Affiliation Jonathan Evans, ETH Zürich
Date, Time 19 March 2012, 15:15-16:15
Location HG G 43
Pseudoholomorphic curves and nilpotent Lie algebras
HG G 43
26 March 2012
15:15-16:30
Dietmar Salamon
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Combinatorial Floer homology
Speaker, Affiliation Dietmar Salamon, ETH Zürich
Date, Time 26 March 2012, 15:15-16:30
Location HG G 43
Abstract Lagrangian Floer homology is an invariant associated, under favourable assumptions, to a pair of Lagrangian submanifolds of a symplectic manifold. The talk discusses a combinatorial approach to Floer theory in the simplest possible setting of two embedded circles in a Riemann surface. It is based on joint work with Vin de Silva and Joel Robbin.
Combinatorial Floer homologyread_more
HG G 43
2 April 2012
15:15-16:30
Felix Schlenk
Université de Neuchâtel
Event Details

Symplectic Geometry Seminar

Title S^1-equivariant Floer homology for hypersurfaces
Speaker, Affiliation Felix Schlenk, Université de Neuchâtel
Date, Time 2 April 2012, 15:15-16:30
Location HG G 43
Abstract We define an S^1-equivariant version of the Floer homology for contact hypersurfaces constructed by Cieliebak and Frauenfelder, and show that this homology vanishes if the hypersurface can be displaced from itself by a Hamiltonian isotopy. This gives obstructions to exact contact embeddings, and sheds some light on the "index positivity problem" for contact hypersurfaces. This is work in progress with Urs Frauenfelder.
S^1-equivariant Floer homology for hypersurfacesread_more
HG G 43
23 April 2012
15:15-16:30
Viktor Ginzburg
UC Santa Cruz, USA
Event Details

Symplectic Geometry Seminar

Title Action-index relations for Hamiltonian dynamical systems
Speaker, Affiliation Viktor Ginzburg, UC Santa Cruz, USA
Date, Time 23 April 2012, 15:15-16:30
Location HG G 43
Abstract In this talk we discuss Hamiltonian diffeomorphisms with finitely many periodic orbits. We show that, under suitable additional hypotheses on the ambient manifold, the actions and mean indexes of periodic orbits of such a diffeomorphism must satisfy certain relations. The talk is based on joint work with Basak Gurel and Mike Chance.
Action-index relations for Hamiltonian dynamical systemsread_more
HG G 43
30 April 2012
15:15-16:30
Peter Albers
Universität Münster
Event Details

Symplectic Geometry Seminar

Title Periodic bounce orbits of prescribed energy
Speaker, Affiliation Peter Albers, Universität Münster
Date, Time 30 April 2012, 15:15-16:30
Location HG G 43
Abstract This is joint work with Marco Mazzucchelli. Periodic bounce orbits are generalizations of billiard trajectories in the presence of a potential. Using an approximation technique by Benci-Giannoni we prove existence of periodic bounce orbits of prescribed energy. At the end of the talk I will sketch very recent work in which we allow much more general Lagrangian systems including magnetic and Finsler billiards.
Periodic bounce orbits of prescribed energyread_more
HG G 43
14 May 2012
15:15-16:30
Dietmar Salamon
ETH Zurich
Event Details

Symplectic Geometry Seminar

Title Hyperkaehler Floer theory, the Fueter equation, and divergence free frames
Speaker, Affiliation Dietmar Salamon, ETH Zurich
Date, Time 14 May 2012, 15:15-16:30
Location HG G 43
Abstract A divergence free frame on a closed three manifold is called regular if every solution of the linear Fueter equation is constant and is called singular otherwise. The set of singular divergence free frames is an analogue of the Maslov cycle. Regular divergence free frames satisfy an analogue of the Arnold conjecture for flat hyperkaehler target manifolds. The Seiberg-Witten equations can be viewed as gauged versions of the Fueter equation, and so can the Donaldson-Thomas equations on certain seven dimensional product manifolds.
Hyperkaehler Floer theory, the Fueter equation, and divergence free framesread_more
HG G 43
21 May 2012
15:15-16:15
Dr. Ana Cannas da Silva
ETH Zürich
Dr. Meike Akveld
ETH Zurich, Switzerland
Event Details

Symplectic Geometry Seminar

Title Lagrangian correspondences - a toric case study
Speaker, Affiliation Dr. Ana Cannas da Silva, ETH Zürich
Dr. Meike Akveld, ETH Zurich, Switzerland
Date, Time 21 May 2012, 15:15-16:15
Location HG G 43
Abstract This is a review talk given jointly by Meike Akveld and Ana Cannas da Silva.
Lagrangian correspondences - a toric case studyread_more
HG G 43

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Organizers: Paul Biran, Ana Cannas da Silva, Dietmar Salamon

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