The size of the largest Erd\H os-Ko-Rado set of generators in the finite classical polar space is known for all polar spaces except for $H(2d-1,q^2)$ when $d\ge 5$ is odd. We improve the known upper bound in this remaining case by using a variant of the famous Hoffman's bound.

Klaus Metsch

For $q>27$ we determine the independence number $\alpha(\Gamma)$ of the Kneser graph $\Gamma$ on plane-solid flags in $PG(6,q)$. More precisely we describe all maximal independent sets of size at least $q^{11}$ and show that every other maximal example has cardinality at most a constant times $q^{10}$.

Klaus Metsch Daniel Werner

We establish the existence and smoothness of minimizers of the Willmore energy among axially symmetric surfaces of spherical type with prescribed isoperimetric ratio. Afterwards, we study the behavior of these minimizers as the isoperimetric ratio tends to zero.

Jan-Henrik Metsch

We consider the optimal transportation problem on a globally hyperbolic spacetime with a cost function $c$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is given by the squared Riemannian distance. Building upon methods of weak KAM theory, we will establish the existence of $C_{loc}^{1,1}$ optimal pairs for the dual optimal transport problem for probability measures along displacement interpolations.

Alec Metsch

We present the results of a covariant constituent quark model, based on the Bethe-Salpeter equation, where confinement is implemented by a string like linear potential explaining the Regge trajectories. An instanton induced quark force explains not only the splitting and mixing of pseudoscalar mesons, but suggest that such effects are also present in the scalar spectrum and in a violation of the OZI rule in the decays of scalar particles into pseudoscalars. We demonstrate that a covariant treatment that takes into account the relativistic components in the amplitudes is of utmost importance when describing properties of deeply bound states and/or processes at higher momentum transfer.

B. C. Metsch H. R. Petry

We present a relativistic quark model for baryons, based on the Bethe-Salpeter equation in instantaneous approximation. Confinement is implemented by an interaction kernel which essentially is a linearly rising potential with a spin-dependence chosen such as to minimize spin-orbit effects. The fine structure of the baryon spectrum follows from an effective quark-interaction based on instanton effects. Results for the spectra of all baryons build from u,d,s-quarks are presented. In particular it is found, that the present relativistic setup can account for the low position of Roper-like resonances in all sectors.

Bernard Metsch

On the basis of the Bethe-Salpeter Equation we developed a covariant constituent quark model, with confinement implemented by a linear potential and an instanton induced interaction explaining mass splittings and mixing of pseudoscalar mesons. In addition this interaction yields a scalar (essentially) flavour singlet state at approximately 1 GeV, considerably lower in mass than the corresponding octet states calculated around 1.4 GeV. The validity of the present approach was checked through various electroweak observables. The puzzling properties of scalar mesons is briefly discussed.

Bernard Metsch

In this contribution I will try to give an overview of what has been achieved in constituent quark models of mesons and baryons by a comparison of some selected results from various ansaetze with experimental data. In particular I will address the role of relativistic covariance, the nature of the effective quark forces, the status of results on electromagnetic and strong-decay observables beyond the mere mass spectra, as well as some unresolved issues in hadron spectroscopy.

Bernard Metsch

We consider the area-preserving Willmore evolution of surfaces that are close to a half-sphere with a small radius, sliding on the boundary S of a domain while meeting it orthogonally. We prove that the flow exists for all times and keeps a 'half-spherical' shape. Additionally, we investigate the asymptotic behaviour of the flow and prove that for large times the barycenter of the surfaces approximately follows an explicit ordinary differential equation. Imposing additional conditions on the mean curvature of S, we then establish convergence of the flow.

Jan-Henrik Metsch

The generalized Kneser graph $K(n,k,t)$ for integers $k>t>0$ and $n>2k-t$ is the graph whose vertices are the $k$-subsets of $\{1,\dots,n\}$ with two vertices adjacent if and only if they share less than $t$ elements. We determine the treewidth of the generalized Kneser graphs $K(n,k,t)$ when $t\ge 2$ and $n$ is sufficiently large compared to $k$. The imposed bound on $n$ is a significant improvement of a previously known bound. One consequence of our result is the following. For each integer $c\ge 1$ there exists a constant $K(c)\ge 2c$ such that $k\ge K(c)$ implies for $t=k-c$ that $$tw(K(n,k,t))=\binom{n}{k}-\binom{n-t}{k-t}-1$$ if and only if $n\ge (t+1)(k+1-t)$ .

Klaus Metsch