## Hauteurs de sous-espaces sur les corps non commutatifs

In analogy to a characterisation of operator matrices generating $C_0$-semigroups due to R. Nagel (\cite{[Na89]}), we give conditions on its entries in order that a $2\times 2$ operator matrix generates a cosine operator function. We apply this to systems of wave equations, to second order initial-boundary value problems, and to overdamped wave equ...

Published in Mathematische Zeitschrift

In their study of diophantine approximation of the exponential function in connection with Sondow’s Conjecture, Berndt et al. (Adv Math 348:1298–1331, 2013) have constructed certain p-adic functions arising from the sequence of convergents to the continued fraction of e. We solve an open problem posed in [2], more precisely we show that those p-adi...

We show that the distributions occurring in the geometric and spectral side of the twisted Arthur-Selberg trace formula extend to non-compactly supported test functions. The geometric assertion is modulo a hypothesis on root systems proven when the group is split. The result extends the work of Finis-Lapid (and M\"uller, spectral side) to the twist...

Published in Mathematische Zeitschrift

We obtain a quantitative estimate on the generalised index of translators for the mean curvature flow with bounded norm of the second fundamental form. The estimate involves the dimension of the space of weighted square integrable f-harmonic 1-forms. By the adaptation to the weighted setting of Li–Tam theory developed in previous works, this yields...

Published in Mathematische Zeitschrift

A one-parameter family of coupled flows depending on a parameter κ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa >0$$\end{document} is introduced which reduce...

For an arbitrary quiver Q = (I, Ω) and dimension vector d ∈ N I we define the dimension of absolutely cuspidal functions on the moduli stacks of representations of dimension d of a quiver Q over a finite field Fq, and prove that it is a polynomial in q, which we conjecture to be positive and integral. We obtain a closed formula for these dimensions...

We provide a characterization of Symplectic Grassmannians in terms of their Varieties of Minimal Rational Tangents.