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.

- 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)*