(Non-)Integrability of calibrated k-plane fields
Montag, 31.10.11, 16:15-17:15, Raum 404, Eckerstr. 1
Destruction of minimal foliations for finite range Frenkel-Kontorova models
Montag, 7.11.11, 16:15-17:15, Raum 404, Eckerstr. 1
Monotone variational recurrence relations such as the Frenkel-\nKontorova lattice, arise in solid state physics and as Hamiltonian\ntwist maps. Aubry-Mather theory guarantees the existence of minimizers\nof every rotation number. They constitute the Aubry-Mather set. When\nthe rotation number is irrational, the Aubry-Mather set is either\nconnected - a foliation, or a Cantor set - a lamination. It turns out\nthat when the rotation number of a minimal foliation is Liouville\n(easy to approximate by rational numbers) the foliation can be\ndestroyed into a lamination by an arbitrarily small smooth\nperturbation of the recurrence relation.
Computing descendants in symplectic field theory
Montag, 21.11.11, 16:00-17:00, Raum 404, Eckerstr. 1
Symplectic field theory (SFT) assigns to each symplectomorphism (of a closed symplectic manifold) an infinite-dimensional Hamiltonian system with an infinite number of symmetries. While the latter are obtained using descendants, for Hamiltonian symplectomorphisms this leads to the well-known integrable hierarchies of Gromov-Witten theory. In joint work with P. Rossi we study the algebraic structure of descendants, both to find richer geometrical invariants and to answer the question of integrability for general symplectomorphisms.
Crepant resolutions of Calabi-Yau orbifolds
Montag, 5.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
A Calabi-Yau orbifold in complex dimension 3 is locally modeled on C^3/G with G a finite subgroup of SL(3,C). When G acts with an isolated fixed point on C^3, a crepant resolution has the structure of an asymptotically locally euclidean (ALE) manifold. Using index theory techniques we derive a geometrical interpretation of the McKay correspondence which relates the geometry of the crepant resolution to the representation theory of the finite group G. This extends a result of Kronheimer and Nakajima to this higher dimensional case.
Matrix models, enumerative geometry and integrability
Montag, 12.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
Some of generating functions in enumerative geometry are known to be related to matrix integrals and \nclassical integrable hierarchies of KP/Toda type. In recent years it become clear that the partition functions of the \nthis still not completely described set of models posses other nice properties such \nas cut-and-join-type representations, random partition descriptions and Virasoro-type constraints. \nI will explain some of the aforementioned properties and relations between them for three important models, namely Hermitian matrix model,\nKontsevich-Witten tau-function and generating function of Hurwitz numbers.
Rigidity of complete Riemannian cylinders without conjugate points
Montag, 19.12.11, 16:15-17:15, Raum 404, Eckerstr. 1
Quadratic Differentials and BPS states
Montag, 9.1.12, 16:15-17:15, Raum 404, Eckerstr. 1
tba
Montag, 16.1.12, 14:15-15:15, Raum 404, Eckerstr. 1
Counting curves on Calabi-Yau manifolds
Montag, 16.1.12, 16:15-17:15, Raum 404, Eckerstr. 1
We give an overview on Gromov-Witten theory of Calabi-Yau manifolds. In particular, we study generating functions of Gromov-Witten invariants and explain their reformulations by physicists. Our focus will lie on those cases for which these functions turn out or are expected to be modular forms.
Invariants of elliptically fibered Calabi-Yau 3-folds
Montag, 23.1.12, 16:15-17:15, Raum 404, Eckerstr. 1
We look at a special type of elliptically fibered Calabi-Yau 3-folds arising via the heterotic/F-theory string-string duality. We describe the imprint of this duality on the geometry and topology of the Calabi-Yaus. This is joint work with Katrin Wendland.
tba
Montag, 30.1.12, 16:15-17:15, Raum 404, Eckerstr. 1
The Family Index Theorem and the Eta-Form
Montag, 6.2.12, 16:15-17:15, Raum 404, Eckerstr. 1
We'll give an overview of the index theorem in different situations and then we'll concentrate on families of closed manifolds. We are interested in the eta-form and its convergence at infinity and zero.\nOur presentation will be based on "Heat Kernels and Dirac Operators" by Berline, Getzler and Vergne.
Kozykel für charakteristische Klassen
Montag, 13.2.12, 16:15-17:15, Raum 404, Eckerstr. 1
In meinem Vortrag konstruiere ich nach Brylinski-Mc Laughlin Kozykeldarstellungen für charakteristische Klassen in der glatten Deligne-Kohomologie.