Please contact Birgit Mehrabadi for accommodation and questions about reimbursement.
Some accomodation at reasonable prices is avaible at the DESY hostel which is at a 40 minutes ride from the mathematics department. Mention "Center for Mathematical Physics" when booking.
The talks will take place in the seminar room to the Klima Campus, Grindelberg 5, near to the math department. It can easily be reached by taking the subway U2 or U3 (both lines also stop at the central station) to the station Schlump and then follow the street "Beim Schlump" (which starts at the station, so the direction is unique) to its end. Then turn left, it is the second or third building on the left hand side (unfortunately, google-maps does not know "Grindelberg 5", the buliding is roughly where google-maps would find "Grindelberg 1").
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Schedule for Saturday 5 December
Schedule for Sunday 6 December
- Alexander Alldridge Harmonic analysis on symmetric superspaces
In the study of large N statistics of random matrix ensembles, embeddings of all of Cartan's
ten infinite series of Riemannian symmetric spaces G/K into complex symmetric superspaces
occur in a natural fashion. This plays a role in applications to mesoscopic physics (e.g. in the work
of Wegner, Efetov, and Zirnbauer).
In this context, questions of harmonic analysis (such as to the validity of a spherical Fourier inversion
theorem for K-invariant functions) arise. This suggests a systematic study of harmonic analysis on
In an ongoing programme with J. Hilgert (Paderborn) and M.R. Zirnbauer (Köln) we are developing
the harmonic analysis of invariant differential operators and spherical functions in this context.
In the talk, I shall explain the framework of our investigation and present our results on the
generalisation Chevalley's restriction theorem, invariant Berezin integration, and their application
to a generalisation of the Harish-Chandra isomorphism. Many new features occur: For instance, the
variety defined by the algebra of symmetric invariants (which is affine the classical case) may be
- Joachim Hilgert: Special functions associated with minimal representations of O(p,q)
We develop a theory of "special functions" associated to a certain fourth order differential operator Dμ,ν on R depending on two parameters μ,ν. For integers μ,ν≥-1 with μ+ν∈2N0 this operator extends to a self-adjoint operator on L2(R+,xμ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, L2-norms, integral representations and various
The fourth order differential operator Dμ,ν arises as the radial part of the Casimir action in the Schrödinger model of the minimal representation of the group O(p,q), and our "special functions" give K-finite vectors.
This is joint work with T. Kobayashi, G. Mano, and J. Möllers.
- Alexey Petukhov:
Connection between k-spherical Grassmanians and spherical (g,k)-modules
Famous article of A.Beilinson and J.Bernstein explains that there is a close connection between modules of a Lie algebra g and a geometry of a
maximal Grassmanian of g - the variety of all Borel subalgebras. Using this connection I'm able to solve a problem introduced by Ivan Penkov and
Vera Serganova - classify all pairs (sln, k) such that there exists a spherical (sln, k)-module.
Theorem. There exists a spherical (sl(V), k)-module if and only if there exists k such that Gr(k, V) is a spherical k-variety.
I proove that if Gr(k, V) is a spherical variety then the variety P(V) is k-spherical too and find out all pairs (k,(g,V))
such that the variety Gr(k, V) is spherical.
Borel-Weil theory for root graded Lie groups over commutative
Root graded Lie groups are generalizations of
semisimple complex Lie groups which are allowed to be infinite
For a root graded Lie group G one can define parabolic subgroups.
Any holomorphic Banach representation of a parabolic subgroup, P,
defines a holomorphic (Banach) vector bundle over
the complex manifold G/P. In particular, a holomorphic character
of P defines a line bundle. We give a characterization of those
line bundles which admit nonzero global holomorphic sections in the case
when G/P is a scalar extension of a compact flag variety by a commutative
This is joint work with Karl-Hermann Neeb.
Gerbes, symmetries and generalised geometry
The presence of the abelian gerbe
G in a rigourous formulation of the two-dimensional conformal
field theory of the string on a metric space (M, g), prerequisite to a non-anomalous realisation of
the conformal symmetry in the quantised theory, significantly modifies the structure of internal
symmetries of the theory in that it puts them in correspondence with Killing sections of the
generalised tangent bundle, rather than Killing vector fields, over the target space M of the
string. The study of a symplectic presentation of these symmetries, formulated in terms of target-
space structures (M, g,
G ) transgressed to the field space of the theory, leads to the emergence
of a general framework of description of stringy symmetries and dualities that uses a 2-category
naturally associated with the gerbe.
In the talk, this general framework will be discussed, alongside some of its field-theoretic and
geometric applications. Time permitting, we shall illustrate our considerations with physically
relevant examples, to wit, the maximally symmetric defect quiver in the Wess-Zumino-Witten
model, the gauged sigma model on a G-space, and the T-duality construction.