Talk

The unit spheres in orthogonal  representations of finite groups give  basic linear examples of group actions on spheres. The talk will be about the connection between finite group theory, and the fixed sets and isotropy subgroups found in actions on spheres. For example, there are finite groups which act freely and smoothly on spheres, but not linearly. The complexity of non-free actions can be measured by the rank of the isotropy subgroups. I will survey previous results and describe my

http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html

Video: 

freedman03.mp4

Research done by information theorists over the past decade has
shown that lattices constructed from rings of integers in number fields,
and orders in division algebras, provide codebooks well-suited for
communication over wireless channels.  In particular, recent work has shown
that when communication over a wireless channel occurs in the presence of
an eavesdropper, one can estimate the eavesdropper's probability of
correctly intercepting the message, using the regulator and Dedekind zeta
function of the underlying number field.  In this talk, we will explain
these basic concepts, and elaborate on ongoing work on wiretap channels.
 This is joint work with Camilla Hollanti and Emanuele Viterbo.

Let k be a global function field. It is a well-known fact that
the first cohomology set of a reductive group over k has an abelian group
structure. In this talk we will show that the first cohomology set of an
arbitrary pseudo-reductive group over k can be naturally embedded in an
abelian group. Under a certain condition, the set in question has a natural
abelian group structure. We will also discuss class groups of wound
unipotent groups of toric type.

Rogers has defined a class of L$_\infty$-algebras that are naturally associated with manifolds equipped with closed higher-degree forms, and that reduce to Poisson bracket Lie algebras in the case of symplectic manifolds. Here we show that these L$_\infty$-algebras can be naturally identified with the L$_\infty$-algebras of infinitesimal autoequivalences of higher prequantum bundles. In particular, they are a Kostant-Souriau-type L$_\infty$ extension of (higher) Hamiltonian symplectomorphisms. By truncation of the connection data for the prequantum bundle, this produces higher analogues of the Lie algebra of sections of the Atiyah algebroid and of the Lie 2-algebra of sections of the Courant Lie 2-algebroid. Restriction along higher moment maps yields L$_\infty$ analogs of the Heisenberg Lie algebra and of the string Lie 2-algebra. Joint work with Christopher Rogers and Urs Schreiber.