Grid homology of knots and links in S^3
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Combinatorial invariants
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Heegaard Floer homologies: topological preliminaries
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Stability Conditions on K3 surfaces (after Bridgeland)
D-equivalence and K-equivalence (after Kawamata)
The Frobenius morphism on homogeneous spaces and cohomology of line bundles in characteristic p
Uniqueness of the contact structure approximating a foliation
According to a theorem of Eliashberg and Thurston a C2-foliation on a closed 3-manifold can be C0-approximated by contact structures unless all leaves of the foliation are spheres. Examples on the 3-torus show that every neighbourhood of a foliation can contain
infinitely many non-diffeomorphic contact structures. In this talk we show that this is rather exceptional: In many interesting situations the contact structure in a sufficiently small
neighbourhood of the foliation is uniquely determined up to isotopy. This fact can be
applied to obtain results about the topology of the space of taut foliations.
Habilitationsvortrag
Introduction to geometry and physics of knot homologies, IV
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Introduction to geometry and physics of knot homologies, III
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Introduction to geometry and physics of knot homologies, II
Introduction to geometry and physics of knot homologies
Pi_1 negligible embeddings in 4-manifolds, and applications
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Pi_1 negligible embeddings in 4-manifolds, and applications
http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html
Twisted cubics on cubic fourfolds
The p-adic monodromy group of abelian varieties over global function fields of characteristic p
We prove an analogue of the Tate isogeny conjecture and the semi-simplicity conjecture for overconvergent crystalline Dieudonne modules of abelian varieties defined over global function fields of characteristic p, combining methods of de Jong and Faltings. As a corollary we deduce that the monodromy groups of such overconvergent crystalline Dieudonne modules are reductive, and after base change to the field of complex numbers they are the same as the monodromy groups of Galois representations on the corresponding l-adic Tate modules, for l different from p.
Invariants of Harish-Chandra Modules
The distribution character is a complete invariant of Harish-Chandra modules
(it determines the representation up to infinitesimal equivalence.) It is very
difficult to compute. There are other invariants, sometimes weaker, which
contain very important information about the representation. An example is
the associated cycle. In the first part of the talk I will introduce some such
invariants and explain relevant information encoded by them. The second part
of the talk, based on work with R. Zierau, will focus on the computation of
associated cycles for a class of representations.
Induced representations of infinite-dimensional groups
Induced representations were introduced and studied by F.G. Frobenius in 1898 for finite groups
and developed by G.W. Mackey (1949) for locally compact groups. We generalize the Mackey construction for infinite-dimensional groups. To do this, we construct some G -quasi-invariant
measures on an appropriate completion of the initial space X=H\G. A.A. Kirillov's orbit method (1962) describes all irreducible unitary representations of the finite-dimensional nilpotent group G in terms of induced representations associated with orbits in coadjoint action of the group G in a
dual space g* of the Lie algebra g. As the illustration we start to develop an analog of the
orbit method for infinite-dimensional ``nilpotent'' group of upper triangular matrices.
The Witten genus and topological modular forms
I will give a fairly high level introduction to topological modular forms (Tmf) and their relationship to the Witten genus. Tmf was constructed, in part, as the target of a cohomological lift of Witten genus. The Witten genus assigns a modular form to a string manifold and this assignment is invariant under string bordism. This is analogous to the A-hat genus which assigns to a spin manifold an elliptic operator which, in turn, defines a formal difference of vector spaces. Moreover the A-hat genus is invariant under spin bordism. Aityah, Bott, and Shapiro demonstrated the A-hat genus lifts to a map of cohomology theories MSpin-->KO. The analogous theory for the Witten genus is the cohomology theory tmf which has been constructed, in several ways, by Mike Hopkins, Haynes Miller, Paul Goerss, and Jacob Lurie. These lifts were constructed and shown to preserve an enormous amount of structure (they are E_\infty maps) by Ando, Hopkins, and Rezk.
Quantum cohomology and quantum groups
We describe the recent research started by Nekrasov, Shatashvili, Braverman, Maulik, Okounkov on correspondence between the quantumcohomology of the quiver varieties and the quantum integrable systems. Our main example will be the quantum cohomology of the cotangent spaces to partial flag varieties and its vis a vis from the representation theory, the quasi periodic Heisenberg spin chain. We will discuss how the both subjects may contribute to each other via this correspondence.
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