Departement Mathematik

Symplectic geometry seminar

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Herbstsemester 2017

Datum / Zeit Referent:in Titel Ort
18. September 2017
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 18. September 2017, 15:15-16:30
Ort
No seminar
25. September 2017
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 25. September 2017, 15:15-16:30
Ort HG G 43
No seminar
HG G 43
2. Oktober 2017
15:15-16:30 		Oscar Garcia-Prada
Instituto de Ciencias Matemáticas, Madrid
Details

Symplectic Geometry Seminar

Titel Special components of Higgs bundle moduli spaces and character varieties
Referent:in, Affiliation Oscar Garcia-Prada, Instituto de Ciencias Matemáticas, Madrid
Datum, Zeit 2. Oktober 2017, 15:15-16:30
Ort HG G 43
Abstract In this talk we consider the moduli space of G-Higgs bundles over a compact Riemann surface X, where G is a real semisimple Lie group. By non-abelian Hodge theory, this space is homeomorphic to the moduli space of representations of the fundamental group of X in G --- the character variety. It is well-known that when G is split or hermitian there are special components that are not detected by the obvious topological invariants (Hitchin and maximal components, respectively), and that are higher rank versions of Teichmueller space. After explaining this, we will show that, quite unexpectedly, this phenomenon also hapens for the group SO(p,q) for arbitrary p and q.
Special components of Higgs bundle moduli spaces and character varietiesread_more
HG G 43
23. Oktober 2017
15:15-16:30 		Jake Solomon
Hebrew University, Israel
Details

Symplectic Geometry Seminar

Titel The space of positive Lagrangians
Referent:in, Affiliation Jake Solomon, Hebrew University, Israel
Datum, Zeit 23. Oktober 2017, 15:15-16:30
Ort HG G 43
Abstract A Lagrangian submanifold of a Calabi-Yau manifold is positive if the real part of the holomorphic volume form restricts on it to a positiveform. A mirror symmetric analogy holds between positive Lagrangians and Hermitian metrics on holomorphic vector bundles or Kähler metrics oncomplex manifolds. Specifically, a Hamiltonian isotopy class of positive Lagrangians admits a Riemannian metric of non-positive sectional curvature and a convex functional which has critical points at special Lagrangians. Geodesics are equivalent to solutions of the degenerate special Lagrangian equation. Existence of geodesics would imply uniqueness of special Lagrangians aswell as a version of the strong Arnold conjecture. Weak geodesics are known to exist between positive graph Lagrangians in Euclidean space. Smooth geodesics can be constructed in Milnor fibers and toric Calabi-Yau manifolds using symmetry techniques. This talk is based partially on joint work with Y. Rubinstein and A. Yuva
The space of positive Lagrangiansread_more
HG G 43
30. Oktober 2017
15:15-16:30 		Paul Biran
ETH Zürich
Details

Symplectic Geometry Seminar

Titel The filtered Fukaya category and its applications
Referent:in, Affiliation Paul Biran, ETH Zürich
Datum, Zeit 30. Oktober 2017, 15:15-16:30
Ort HG G 43
The filtered Fukaya category and its applications
HG G 43
6. November 2017
15:15-16:30
Details

Symplectic Geometry Seminar

Titel No seminar
Referent:in, Affiliation
Datum, Zeit 6. November 2017, 15:15-16:30
Ort HG G 43
No seminar
HG G 43
20. November 2017
15:15-16:30 		Dr. Urs Fuchs
Universität Heidelberg
Details

Symplectic Geometry Seminar

Titel Gromov compactness for pseudoholomorphic curves
Referent:in, Affiliation Dr. Urs Fuchs, Universität Heidelberg
Datum, Zeit 20. November 2017, 15:15-16:30
Ort HG G 43
Abstract In this talk I will show how Gromov's compactness result for closed pseudoholomorphic curves is proved by studying the (possibly degenerate) induced conformal metrics on the curves. I will then discuss for which type of boundary conditions one can expect (and prove) a compactness result for stable pseudoholomorphic curve with boundary.
Gromov compactness for pseudoholomorphic curvesread_more
HG G 43
27. November 2017
15:15-16:30 		Charlotte Kirchhoff-Lukat
University of Cambridge, UK
Details

Symplectic Geometry Seminar

Titel Branes with boundary and symplectic methods for stable generalised complex manifolds
Referent:in, Affiliation Charlotte Kirchhoff-Lukat, University of Cambridge, UK
Datum, Zeit 27. November 2017, 15:15-16:30
Ort HG G 43
Abstract Generalised complex geometry (introduced by Hitchin and Gualtieri in the early 2000's) interpolates between ordinary complex and symplectic geometry. Stable generalised complex manifolds (first introduced by Cavalcanti and Gualtieri in 2015) provide a class of examples of generalised complex manifolds that admits neither a symplectic nor a complex structure. Their generalised complex structure is, up to gauge equivalence, fully determined by a Poisson structure which is symplectic everywhere except on a real codimension 2 submanifold. I will describe how to generalise a range of symplectic techniques to these manifolds, and describe their natural generically Lagrangian submanifolds, in particular a new type called Lagrangian brane with boundary. I will discuss local deformations and how such branes might arise as objects of of a Fukaya category for certain stable generalised complex manifolds.
Branes with boundary and symplectic methods for stable generalised complex manifoldsread_more
HG G 43
4. Dezember 2017
15:15-16:15 		Dr. Igor Uljarevic
Tel Aviv University, Israel
Details

Symplectic Geometry Seminar

Titel Floer homology and contact Hamiltonians
Referent:in, Affiliation Dr. Igor Uljarevic, Tel Aviv University, Israel
Datum, Zeit 4. Dezember 2017, 15:15-16:15
Ort HG G 43
Floer homology and contact Hamiltonians
HG G 43
11. Dezember 2017
15:15-16:15 		Yoel Groman
Columbia University, USA
Details

Symplectic Geometry Seminar

Titel Wrapped Floer theory and Homological mirror symmetry for toric Calabi-Yau manifolds
Referent:in, Affiliation Yoel Groman, Columbia University, USA
Datum, Zeit 11. Dezember 2017, 15:15-16:15
Ort HG G 43
Abstract I will discuss how to construct the wrapped Fukaya category of Lagrangian torus fibration a la SYZ over a non compact base. This includes cases which are not exact near infinity. I will use this to formulate the homological mirror symmetry conjecture for this setting at least under favorable assumptions. For the case where the A-model is the complement of an anti-canonical divisor in a toric Calabi Yau manifold, I will discuss how to compute the Floer homology of a Lagrangian section and use it to prove homological mirror symmetry for this case.
Wrapped Floer theory and Homological mirror symmetry for toric Calabi-Yau manifoldsread_more
HG G 43

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