ETH :: D-MATH :: Symplectic Geometry Seminar

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.

Speakers:

Prof. Dr. Johannes Walcher (McGill University, Canada)

20-feb-2012 (mon)

Georgios Rizell

Knotted Legendrian surfaces with few Reeb chords

15:15-16:30

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.

Speakers:

Georgios Rizell (Uppsala University, Sweden)

27-feb-2012 (mon)

Paolo Rossi

Non equivariant contact homology revisited: a Poisson-Nijenhuis structure in SFT

15:15-16:30

HG G 43

Speakers:

Paolo Rossi (University of Zurich)

19-mar-2012 (mon)

Jonathan Evans

Pseudoholomorphic curves and nilpotent Lie algebras

15:15-16:15

HG G 43

Speakers:

Jonathan Evans (ETH Zürich)

26-mar-2012 (mon)

Dietmar Salamon

Combinatorial Floer homology

15:15-16:30

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.

Speakers:

Dietmar Salamon (ETH Zürich)

2-apr-2012 (mon)

Felix Schlenk

S^1-equivariant Floer homology for hypersurfaces

15:15-16:30

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.

Speakers:

Felix Schlenk (Université de Neuchâtel)

23-apr-2012 (mon)

Viktor Ginzburg

Action-index relations for Hamiltonian dynamical systems

15:15-16:30

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.

Speakers:

Viktor Ginzburg (UC Santa Cruz, USA)

30-apr-2012 (mon)

Peter Albers

Periodic bounce orbits of prescribed energy

15:15-16:30

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.

Speakers:

Peter Albers (Universität Münster)

14-may-2012 (mon)

Dietmar Salamon

Hyperkaehler Floer theory, the Fueter equation, and divergence free frames

15:15-16:30

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.

Speakers:

Dietmar Salamon (ETH Zurich)

21-may-2012 (mon)

Ana Cannas da Silva

Meike Akveld

Lagrangian correspondences - a toric case study

15:15-16:15

HG G 43

Abstract:

This is a review talk given jointly by Meike Akveld and Ana Cannas da Silva.

Speakers:

Dr. Ana Cannas da Silva (ETH Zürich)

Dr. Meike Akveld (ETH Zürich, Switzerland)

E-Mail:

Homepage: http://www.math.ethz.ch/people/akveld

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