Research Seminar (Continuing Class)
|Talks in the winter term 2019/2020|
Unless otherwise stated the talks take place in room 2.066 in the "Kollegiengebäude Mathematik" (20.30) from 14:00 to 15:30.
|15.10.2019||Nick Lindemulder (Karlsruhe)||An Intersection Representation for a Class of Anisotropic Vector-valued Function Spaces|
In this talk we discuss an intersection representation for a class of anisotropic vector-valued function spaces in an axiomatic setting à la Hedberg & Netrusov, which includes weighted anisotropic mixed-norm Besov and Triebel-Lizorkin spaces. In the special case of the classical Triebel-Lizorkin spaces, the intersection representation gives an improvement of the well-known Fubini property. The motivation comes from the weighted -maximal regularity problem for parabolic boundary value problems, where weighted anisotropic mixed-norm Triebel-Lizorkin spaces occur as spaces of boundary data.
|22.10.2019||Bas Nieraeth (Karlsruhe)||Weighted theory and extrapolation for multilinear operators|
|19.11.2019||Andreas Geyer-Schulz (Karlsruhe)||On global well-posedness of the Maxwell–Schrödinger system|
|02.12.2019||Wenqi Zhang (Canberra)||Localisation of eigenfunctions via an effective potential for Schrödinger operators|
For Schrödinger operators with potentials (possibly random) we introduce the Landscape function as an effective potential. Due to the nicer properties of this Landscape function we are able to recover localisation estimates for continuous potentials, and specialise these estimates to obtain an approximate diagonalisation. We give a brief sketch of these arguments.
This talk takes place in seminar room 2.066 at 10.30 am.
|03.12.2019||Yonas Mesfun (Darmstadt)|| On the stability of a chemotaxis system with logistic growth|
In this talk we are concerned with the asymptotic behavior of the solution to a certain Neumann initial-boundary value problem which is a variant of the so-called Keller-Segel model describing chemotaxis. Chemotaxis is the directed movement of cells in response to an external chemical signal and plays an important role in various biochemical processes such as e.g. cancer growth.
We show a result due to Winkler which says that under specific conditions, there exists a unique classical solution to this Neumann problem which converges to the equilibrium solution with respect to the -norm. For this purpose we study the Neumann Laplacian in , in particular some decay properties of its semigroup and embedding properties of the domain of its fractional powers, and then use those properties to prove Winkler's result.
|10.12.2019||Emiel Lorist (Delft)|| Singular stochastic integral operators: The vector-valued and the mixed-norm approach|
Singular integral operators play a prominent role in harmonic analysis. By replacing integration with respect to some measure by integration with respect to Brownian motion, one obtains stochastic singular integral operators, which arise naturally in questions related to stochastic PDEs. In this talk I will introduce Calderón-Zygmund theory for these singular stochastic integral operators from both a vector-valued and a mixed-norm viewpoint.
|14.01.2020||Alex Amenta (Bonn)|| Vector-valued time-frequency analysis and the bilinear Hilbert transform|
The bilinear Hilbert transform is a bilinear singular integral operator (or Fourier multiplier) which is invariant not only under translations and dilations, but also under modulations. This additional symmetry turns out to make proving -bounds especially difficult. I will give an overview of how time-frequency analysis is used in proving these -bounds, with focus on the recently understood setting of functions valued in UMD Banach spaces.
|21.01.2020||Willem van Zuijlen (Berlin)|| Spectral asymptotics of the Anderson Hamiltonian|
In this talk I will discuss the asymptotics of the eigenvalues of the Anderson Hamiltonian, which is the operator given by . We consider to be (a realisation of) white noise and consider the operator on a box with Dirichlet boundary conditions. I will discuss the result in joint work with Khalil Chouk: almost surely the eigenvalues divided by the logarithm of the size of the box converge to the same limit. I will also discuss the application of this to obtain the large-time asymptotics of the total mass of the parabolic Anderson model, which is the SPDE given by .
|18.02.2020||TULKKA in Konstanz|
The workshop is taking place in room A 704 (University of Konstanz).
|11:45-12:15||Adrian Spener (Ulm)||Curvature-dimension inequalities for nonlocal operators|
|13:45-14:30||Sophia Rau (Konstanz)||Stability results for thermoelastic plate-membrane systems|
|14:45-15:30||Andreas Geyer-Schulz (Karlsruhe)||On global well-posedness of the Maxwell-Schrödinger system|
|16:15-17:00||Delio Mugnolo (Hagen)||Linear hyperbolic systems|
You find previous talks in the archive of the research seminar.