Pure Mathematics
Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.
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On well quasi-order of graph classes under homomorphic image orderings
(2017-06) - Journal articleIn this paper we consider the question of well quasi-order for classes defined by a single obstruction within the classes of all graphs, digraphs and tournaments, under the homomorphic image ordering (in both its standard ... -
Enumerating transformation semigroups
(2017-08) - Journal articleWe describe general methods for enumerating subsemigroups of finite semigroups and techniques to improve the algorithmic efficiency of the calculations. As a particular application we use our algorithms to enumerate all ... -
Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems
(2017-09-07) - Journal articleFor a measure-preserving dynamical system (X, ƒ, μ), we consider the time series of maxima Mn = max{X1,…,Xn} associated to the process Xn = φ (ƒn-1(x)) generated by the dynamical system for some observable φ : Χ → R . Using ... -
The cycle polynomial of a permutation group
(2018-01-25) - Journal articleThe cycle polynomial of a finite permutation group G is the generating function for the number of elements of G with a given number of cycles.In the first part of the paper, we develop basic properties of this polynomial, ... -
Affine rigidity and conics at infinity
(2017-02-26) - Journal articleWe prove that if a framework of a graph is neighborhood affine rigid in d-dimensions (or has the stronger property of having an equilibrium stress matrix of rank n — d — 1) then it has an affine flex (an affine, but non ...
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