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Workgroup Functional Analysis

Kollegiengebäude Mathematik (20.30)
Room 2.041

Karlsruher Institut für Technologie
Institut für Analysis
Englerstraße 2
76131 Karlsruhe

samira.junge@kit.edu, natascha.katz@kit.edu

Office hours:
9:00 - 11:00

Tel.: +49 721 608 43727

Fax.: +49 721 608 67650

Research Seminar (Continuing Class)

Talks in the winter semester 2017/2018

Unless otherwise stated the talks take place in room 2.066 in the "Kollegiengebäude Mathematik" (20.30) from 14:00 to 15:30.

21.05.2019Lucrezia Cossetti (Karlsruhe) Multipliers method for Spectral Theory.
Originally arisen to understand characterizing properties connected with dispersive phenomena, in the last decades the multipliers method has been recognized as a useful tool in Spectral Theory, in particular in connection with proof of absence of point spectrum for both self-adjoint and non self-adjoint operators.
Starting from recovering very well known facts about the spectrum of the free Laplacian H_0=-\Delta in L^2(\mathbb{R}^d), we will see the developments of the method reviewing some recent results concerning self-adjoint and non self-adjoint perturbations of this Hamiltonian in different settings, specifically both when the configuration space is the whole Euclidean space \mathbb{R}^d and when we restrict to domains with boundary. We will show how this technique allows to detect physically natural repulsive and smallness conditions on the potentials which guarantee the absence of eigenvalues. Some very recent results concerning Pauli and Dirac operators will be presented too.
The talk is based on joint works with L. Fanelli and D. Krejcirik.
28.05.2019Philipp Harms (Freiburg)Smoothness of the functional calculus and applications to variational PDEs.
The functional calculus, which maps operators A to functionals f(A), is holomorphic for a certain class of operators A and holomorphic functions f. In particular, fractional Laplacians depend real analytically on the underlying Riemannian metric in suitable Sobolev topologies. As an application, this can be used to prove local well-posedness of some geometric PDEs, which arise as geodesic equations of fractional order Sobolev metrics.
Joint work with Martins Bruveris, Martin Bauer, and Peter W. Michor.

You find previous talks in the archive of the research seminar.