Termine

Let A be a suitably nice C*-algebra (for example, quasidiagonal with countable K-homology). I will explain how the K-homology of A can be realized by almost multiplicative ucp maps to matrices. I?ll sketch some applications to K-homology of spaces, and to approximate representation theory of groups.

Markus Stroppel will give a lecture series on advanced topics in locally compact groups. The lectures take place on Monday at 14:15 in room SR 1D They will start on Monday, November 17. The planned topics are: * the scale function and tidy subgroups * automorphism groups of trees

Abstract: The signature of a closed manifold is an important invariant in geometric topology. Recently, Higson, Xie, and Schick proved an invariance theorem for the K-theoretic signature in codimension 2. However, the L-theoretic counterpart of this result remains an open problem. In this talk, I will describe how to achieve the L-theoretic counterpart of their result and provide some examples. I will also explain the basic ideas of the proof, highlighting the key steps and challenges involved.

At the core of differential geometry is the notion that the important features of a space should remain invariant under changes of coordinates. Nevertheless, spaces with special structure may admit preferred coordinate systems, highlighting some of its features with particular clarity. Such distinguished parameterisations have often been found by identifying a foliation of the space by submanifolds canonically determined by its geometry. An example is foliations by constant mean curvature (CMC) hypersurfaces, which have been used for instance to parameterise the ends of asymptotically flat manifold, leading to a definition of center of mass for isolated gravitating systems. They also played a crucial role in the first proof of the stability of Minkowski spacetime, or in foliating geometric ?necks? to continue geometric flows through neck singularities via surgery. In the codimension $n \ge 2$ setting, the situation is more complicated. Indeed, where the CMC condition would naturally be replaced by Parallel Mean Curvature (PMC), there are generic geometric obstructions for the establishment of such a foliation. In this work, we introduce a new, pseudodifferential, curvature condition, which we dub ?Quasi-Parallel Mean Curvature? (QPMC), and find that bubblesheet singularities (the higher codimension counterpart to necks) can be foliated by QPMC embedded spheres. I will present this curvature condition and the construction of the foliation, as well as examples that indicate the necessity of such a condition. Time permitting, I may present some applications to Mean Curvature Flow.

Harmonic morphisms are maps $\phi:(M,g)\to (N,h)$ between Riemannian manifolds pulling back harmonic functions on N to harmonic functions on M. They have been characterised as being harmonic maps which are horizontally conformal. Under certain natural conditions they induce a conformal foliation on M with minimal leaves. In this talk we will give a short introduction to the general theory. Then we will described what is known in the important cases when M is a Lie group foliated in this way by the left translations of a semisimple subgroup of M.

Kac-Moody groups form an infinite-dimensional generalization of reductive groups, constructed from infinite root systems. For instance, loop groups of reductive groups are Kac-Moody groups. Whereas their behavior over finite or complex fields is very similar to the reductive setting, many constructions fall apart over p-adic or function fields. In this first talk, I will present a building theoretic approach to this problem and introduce the Kac-Moody analog to affine Weyl groups. Even though these are no longer Coxeter groups, they present combinatorial similarities which I will discuss.

The Lagrangian of the Standard Model of particle physics consists of four sectors: the Yang-Mills, the Higgs, the Dirac, and the Yukawa sector. In this talk we study the Dirac-Yang-Mills (DYM) sector in isolation in the Riemannian setting. Variation of the Lagrangian leads to a system of partial differential equations, called the DYM equations, and whose solutions are referred to as DYM pairs. Our goal is to study spherically symmetric DYM pairs on with structure group SU(2), on Riemannian manifolds of dimension 3. In particular, we will systematically obtain the most general spherically symmetric ansatz, which turns the DYM equations into a system of non-autonomous ODEs. We will then construct several different families of solutions to this system, leading to new examples Dirac-Yang-Mills pairs (most notably also on closed manifolds). This is joint work with Adam Lindström.