Janne Kool

• Researcher at Wageningen University & Research

p>Spider mites are one of the most challenging pests in the greenhouse, and their management is more and more challenging due to resistance to pesticides. Spider mites prefer young leaves at the outer canopy, stay at the bottom of leaves, and can crawl to nearby plants. Typical symptoms are small yellow and white spots on the upper side of the leaf...

We present measure theoretic rigidity for graphs of first Betti number b>1 in terms of measures on the boundary of a 2b-regular tree, that we make explicit in terms of the edge-adjacency and closed-walk structure of the graph. We prove that edge-reconstruction of the entire graph is equivalent to that of the "closed walk lengths".

We present measure theoretic rigidity for graphs of first Betti number b>1 in terms of measures on the boundary of a 2b-regular tree, that we make explicit in terms of the edge-adjacency and closed-walk structure of the graph. We prove that edge-reconstruction of the entire graph is equivalent to that of the "closed walk lengths".

We show that if a graph G has average degree $\bar d \geq 4$, then the Ihara zeta function of G is edge-reconstructible. We prove some general spectral properties of the Bass-Hashimoto edge adjancency operator T: it is symmetric on a Krein space and has a "large" semi-simple part (but it can fail to be semi-simple in general). We prove that this im...

We construct explicitly an infinite family of Ramanujan graphs which are bipartite and biregular. Our construction starts with the Bruhat-Tits building of an inner form of $SU_3(\mathbb Q_p)$. To make the graphs finite, we take successive quotients by infinitely many discrete co-compact subgroups of decreasing size.

Let $\Gamma $ be a compact metric graph, and denote by $\Delta $ the Laplace operator on $\Gamma $ with the first non-trivial eigenvalue $\lambda _1$. We prove the following Yang–Li–Yau-type inequality on divisorial gonality $\gamma _{{\rm div}}$ of $\Gamma $. There is a universal (explicit) constant $C$ such that \[ \gamma_{\rm div}(\Gamma) \geq C...

We study the Galois-module structure of polydifferentials on Mumford curves, defined over a field of positive charactersitic. We give the complete structure for the Subrao curves using the theory of harmonic cocycles.

We describe a number of approaches to a question posed by Philips Research, described as the “random disc thrower” problem. Given a square grid of points in the plane, we cover the points by equal-sized planar discs according to the following random process. At each step, a random point of the grid is chosen from the set of uncovered points as the...

We present a method to control gonality of nonarchimedean curves based on graph theory. Let K denote the fraction field of an excellent discrete valuation ring. We first prove a lower bound for the gonality of a curve over the algebraic closure of K in terms of the minimal degree of a class of graph maps, namely: one should minimize over all so-cal...

We study dynamical systems using measures taking values in a non-Archimedean field. The underlying space for such measure is a zero-dimensional topological space. In this paper we elaborate on the natural translation of several notions, e.g., probability measures, isomorphic transformations, entropy, from classical dynamical systems to a non-Archim...

One can describe isomorphism of two compact hyperbolic Riemann surfaces of the same genus by a measure-theoretic property: a chosen isomorphism of their fundamental groups corresponds to a homeomorphism on the boundary of the Poincar\'e disc that is absolutely continuous for Lebesgue measure if and only if the surfaces are isomorphic. In this paper...