We show that the connected component of the embedding space of links in R^3 containing the split union of m Hopf links and n unknots is homotopy equivalent to a parametrised 'round' subspace, extending work of Brendle Hatcher on the unknot case. We discuss potential generalisations and applications.This is joint work with Corey Bregman.
Oberseminar Differentialgeometrie: Maximilian Stegemeyer (Würzburg): Endpoint geodesics in extrinsic symmetric spaces
Montag, 27.01.2020 14:15 im Raum SR2
"In this talk the geodesic equation in symmetric spaces is considered as a boundary value problem.
We show that in extrinsic symmetric spaces this problem can be reduced to solving a matrix equation.
Extrinsic symmetric spaces are symmetric spaces that admit a special isometric embedding into a Euclidean vector space.
Some geometric properties of these spaces will also be mentioned."
Oberseminar Differentialgeometrie: Jason Ledwidge (Tübingen): The structure of non-compact shrinking Ricci solitons via heat kernel estimates
Montag, 27.01.2020 16:15 im Raum SR4
Ricci solitons are solutions to the Ricci flow modulo a diffeomorphism, and arise as singularity models for the Ricci flow. In this talk, we will outline the proof of the uniqueness of the conjugate heat kernel on non-compact shrinking Ricci solitons, without any a priori curvature or volume assumptions. We then use the uniqueness of the conjugate heat kernel to prove that Perelman's celebrated Entropy functional has a unique minimiser on shrinking Ricci solitons. Consequently, this shows that the Riemann tensor is bounded with quadratic decay and that the injectivity radius is bounded from below. These geometric conditions imply shrinking solitons have a unique tangent cone at infinity.
Anton Wakolbinger, Frankfurt: A decomposition of the Brownian excursion (Oberseminar Mathematische Stochastik)
Mittwoch, 29.01.2020 17:00 im Raum SRZ 117
We discuss a realizationwise correspondence between a Brownian excursion (conditioned to reach height one) and a triple consisting of
(1) the local time profile of the excursion,
(2) an array of independent time-homogeneous Poisson processes on the real line, and
(3) a fair coin tossing sequence,
where (2) and (3) encode the ordering by height respectively the left-right ordering of the subexcursions.
The three components turn out to be independent, with (1) giving a time change that is responsible for the time-homogeneity of the Poisson processes. By the Ray-Knight theorem, (1) is the excursion of a Feller branching diffusion; thus the metric structure associated with (2), which generates the so-called lookdown space, can be seen as representing the genealogy underlying the Feller branching diffusion. We will relate our approach also to earlier work of Aldous and Warren on Brownian excursions conditioned on their local time profile.
The lecture is based on joint work with Stephan Gufler and Goetz Kersting.
Kolloquium Wilhelm Killing: Prof. Dr. Assaf Rinot (Bar-Ilan): Hindman's theorem and uncountable Abelian groups
Donnerstag, 30.01.2020 16:30 im Raum M5
In the early 1970's, Hindman proved a beautiful theorem in additive Ramsey theory asserting that for any partition of the set of natural numbers into finitely many cells, there exists some infinite set such that all of its finite sums belong to a single cell.
In this talk, we shall address generalizations of this statement to the realm of the uncountable. Among other things, we shall present a negative partition relation for the real line which simultaneously generalizes a recent theorem of Hindman, Leader and Strauss, and a classic theorem of Galvin and Shelah.
Time permits, we shall also discuss the challenges arising in obtaining similar results for non-Abelian groups.
This is joint work with David Fernandez-Breton.