# Publications

## Finite cyclicity of the contact point in slow-fast integrable systems of Darboux type Hasselt University

Using singular perturbation theory and family blow-up we prove that nilpotent contact points in deformations of slow-fast Darboux integrable systems have finite cyclicity. The deformations are smooth or analytic depending on the region in the parameter space. This paper is a natural continuation of [3, 1] where one studies limit cycles in polynomial deformations of slow-fast Darboux integrable systems, around the "integrable" direction in the ...

## Motivic concentration theorem Hasselt University

In this short article, given a smooth diagonalizable group scheme G of finite type acting on a smooth quasi-compact separated scheme X, we prove that (after inverting some elements of representation ring of G) all the information concerning the additive invariants of the quotient stack [X/G] is "concentrated" in the subscheme of G-fixed points X-G. Moreover, in the particular case where G is connected and the action has finite stabilizers, we ...

## Reconstruction of tensor categories from their structure invariants Hasselt University

In this paper, we study tensor (or monoidal) categories of finite rank over an algebraically closed field F. Given a tensor category C, we have two structure invariants of C: the Green ring (or the representation ring) r(C) and the Auslander algebra A(C) of C. We show that a Krull-Schmit abelian tensor category C of finite rank is uniquely determined (up to tensor equivalences) by its two structure invariants and the associated associator system ...

## A Characterization of Circle Graphs in Terms of Multimatroid Representations Hasselt University

The isotropic matroid M[IAS(G)] of a looped simple graph G is a binary matroid equivalent to the isotropic system of G. In general, M[IAS(G)] is not regular, so it cannot be represented over fields of characteristic not equal 2. The ground set of M[IAS(G)] is denoted W(G); it is partitioned into 3-element subsets corresponding to the vertices of G. When the rank function of M[IAS(G)] is restricted to subtransversals of this partition, the ...

## Spectral identities and smoothing estimates for evolution operators Ghent University

Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the existence (and weak continuity) of the spectral density in a functional setting. Spectral identities for the time evolution of such operators are derived, enabling results concerning U+201Cbest constantsU+201D for smoothing estimates. When combined with suitable U+201Ccomparison ...

## Polyhedra with few 3-cuts are hamiltonian Ghent University

In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four 3-cuts have a hamiltonian path. It is well known that for each k U+2265 6 non-hamiltonian polyhedra with k 3-cuts exist. We give ...

## On the smallest snarks with oddness 4 and connectivity 2 KU Leuven Ghent University

## On a higher structure on operadic deformation complexes University of Antwerp

In this paper, we prove that there is a canonical homotopy (n+1)-algebra structure on the shifted operadic deformation complex $\Def(e_n\to\mathcal{P})[-n]$ for any operad $\mathcal{P}$ and a map of operads $f\colon e_n\to\mathcal{P}$. This result generalizes a result of Tamarkin, who considered the case $\mathcal{P}=\End_\Op(X)$. Another more computational proof of the same result was recently sketched by Calaque and Willwacher. Our method ...

## Proof of a conjecture of Graham and Lovász concerning unimodality of coefficients of the distance characteristic polynomial of a tree Ghent University

The conjecture of Graham and Lovasz that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal is proved; it is also shown that the (normalized) coefficients are log-concave. Upper and lower bounds on the location of the peak are established.