Groningen-Oldenburg-Utrecht mathematical physics seminar

An international intercity seminar

Friday, 16 February 2024, 11:00–17:00, Room 5159.0062 in the Energy Academy Europe building (Groningen)

Please register your participation here. The registration is free and will help us to arrange the catering.

Program of the day

11.00–11:30 registration
 
11.30–12:30 Badreddine Benhellal (University of Oldenburg)

On Neumann-Poincaré operators and self-adjoint transmission problems [slides]

In this talk, we discuss the self-adjointness in $L^2$-setting of the operators acting as $−\mathrm{div} \cdot h\nabla$, with piecewise constant functions $h$ having a jump along a Lipschitz hypersurface $\Sigma$, without explicit assumptions on the sign of $h$. We establish a number of sufficient conditions for the selfadjointness of the operator with $H^{\frac{3}{2}}$-regularity in terms of the jump value and the regularity and geometric properties of $\Sigma$. An important intermediate step is a link with Fredholm properties of the Neumann-Poincaré operator on $\Sigma$, which is new for the Lipschitz setting. Based on joint work with Konstantin Pankrashkin.

12:30–14:00 lunch (Food Court, campus canteen)
 
14:00–15:00 Martijn Kluitenberg (University of Groningen)

Cheeger's inequality in Carnot-Carathéodory spaces [slides]

We explore extending the classical Cheeger inequality to Carnot-Carathéodory (CC) spaces, which are manifolds in which shortest paths can only take velocities confined to a sub-bundle of the tangent bundle. During the talk, I will discuss CC-spaces and their basic properties, as well as the key geometric and analytic concepts used in the proof of Cheeger's inequality. Based on [arXiv:2312.13058].

15:00–15:15 coffee break
 
15:15–16:15 Ruben Zeitoun (Cergy Paris Université)

The wave resolvent for compactly supported perturbations of static spacetimes

I will give an elementary microlocal proof of the essential self-adjointness of the Lorentzian Laplace-Beltrami operator $P$ in the case of compactly supported perturbations of static spacetimes. A modification of the proof also yields uniform microlocal estimates for the resolvent, which serve to prove a relationship between functions of $P$ (in particular the complex powers) and local geometric invariants (following a similar result due to Dang-Wrochna).

16:15– drinks

Organizers: Konstantin Pankrashkin (Oldenburg), Marcello Seri (Groningen) and Michal Wrochna (Utrecht)