## Publications

48 results found

Evans DM, Hubicka J, Konecny M,
et al., 2021, Simplicity of the automorphism groups of generalised metric spaces, *JOURNAL OF ALGEBRA*, Vol: 584, Pages: 163-179, ISSN: 0021-8693

Evans DM, Hubicka J, Nesetril J, 2021, Ramsey properties and extending partial automorphisms for classes of finite structures, *FUNDAMENTA MATHEMATICAE*, Vol: 253, Pages: 121-153, ISSN: 0016-2736

Evans DM, Hubicka J, Konecny M,
et al., 2020, EPPA FOR TWO-GRAPHS AND ANTIPODAL METRIC SPACES, *PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY*, Vol: 148, Pages: 1901-1915, ISSN: 0002-9939

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- Citations: 1

Bridson MR, Evans DM, Liebeck MW,
et al., 2019, Algorithms determining finite simple images of finitely presented groups, *Inventiones Mathematicae*, Vol: 218, Pages: 623-648, ISSN: 0020-9910

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups, or contains classical groups of unbounded dimensions, we prove that there is no such algorithm. On the other hand, for families of simple groups of Lie type of bounded rank, we obtain positive results. For example, for any fixed untwisted Lie type X there is an algorithm that determines whether or not any given finitely presented group has simple images of the form X(q) for infinitely many q, and if there are finitely many, the algorithm determines them.

Evans DM, Hubička J, Nešetřil J, 2019, Automorphism groups and Ramsey properties of sparse graphs, *Proceedings of the London Mathematical Society*, Vol: 119, Pages: 515-546, ISSN: 1460-244X

We study automorphism groups of sparse graphs from the viewpoint oftopological dynamics and the Kechris, Pestov, Todor\v{c}evi\'c correspondence. We investigate amenable and extremely amenable subgroups of these groups using the space of orientations of the graph and results from structural Ramsey theory. Resolving one of the open questions in the area, we show that Hrushovski's example of an $\omega$-categorical sparse graph has no $\omega$-categorical expansion with extremely amenable automorphism group.

Coleman TDH, Evans DM, Gray RD, 2019, Permutation monoids and MB-homogeneous structures, *European Journal of Combinatorics*, Vol: 78, Pages: 163-189, ISSN: 0195-6698

In this paper we investigate the connection between infinite permutation monoids and bimorphism monoids of first-order structures. Taking our lead from the study of automorphism groups of structures as infinite permutation groups and the more recent developments in the field of homomorphism-homogeneous structures, we establish a series of results that underline this connection. Of particular interest is the idea of MB-homogeneity; a relational structure is MB-homogeneous if every monomorphism between finite substructures of extends to a bimorphism of . The results in question include a characterisation of closed permutation monoids, a Fraïssé-like theorem for MB-homogeneous structures, and the construction of pairwise non-isomorphic countable MB-homogeneous graphs. We prove that any finite group arises as the automorphism group of some MB-homogeneous graph and use this to construct oligomorphic permutation monoids with any given finite group of units. We also consider MB-homogeneity for various well-known examples of homogeneous structures and in particular give a complete classification of countable homogeneous undirected graphs that are also MB-homogeneous.

Bodirsky M, Evans D, Kompatscher M,
et al., 2018, A counterexample to the reconstruction of ω-categorical structures from their endomorphism monoid., *Israel Journal of Mathematics*, Vol: 224, Pages: 57-82, ISSN: 0021-2172

© 2018, Hebrew University of Jerusalem. We present an example of two countable ω-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids—in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable ω-categorical structure in a finite relational language which can neither be reconstructed up to first-order biinterpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone.

Evans DM, Tsankov T, 2016, Free actions of free groups on countable structures and property (T), *Fundamenta Mathematicae*, Vol: 232, Pages: 49-63, ISSN: 1730-6329

We show that if G is a non-archimedean, Roelcke precompact Polish group, then G has Kazhdan's property (T). Moreover, if G has a smallest open subgroup of finite index, then G has a finite Kazhdan set. Examples of such G include automorphism groups of countable ω-categorical structures, that is, the closed, oligomorphic permutation groups on a countable set. The proof uses work of the second author on the unitary representations of such groups, together with a separation result for infinite permutation groups. The latter allows the construction of a non-abelian free subgroup of G acting freely in all infinite transitive permutation representations of G.

Evans DM, Ghadernezhad Z, Tent K, 2016, Simplicity of the automorphism groups of some Hrushovski constructions, *Annals of Pure and Applied Logic*, Vol: 167, Pages: 22-48, ISSN: 1873-2461

We show that the automorphism groups of certain countable structures obtained using the Hrushovski amalgamation method are simple groups. The structures we consider are the ‘uncollapsed’ structures of infinite Morley rank obtained by the ab initio construction and the (unstable) ℵ0-categorical pseudoplanes. The simplicity of the automorphism groups of these follows from results which generalize work of Lascar and of Tent and Ziegler.

Amato D, Evans DM, 2015, Infinite primitive and distance transitive directed graphs of finite out-valency, *Journal of Combinatorial Theory Series B*, Vol: 114, Pages: 33-50, ISSN: 1096-0902

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In particular, we show that there are only countably many possibilities for the isomorphism type of such a descendant set, thereby confirming a conjecture of the first Author. As a partial converse, we show that certain related conditions on a countable digraph are sufficient for it to occur as the descendant set of a primitive, distance transitive digraph.

Amato D, Evans DM, Truss JK, 2012, Classification of some countable descendant-homogeneous digraphs, *Discrete Mathematics*, Vol: 312, Pages: 911-919, ISSN: 0012-365X

For finite q, we classify the countable, descendant-homogeneous digraphs in which the descendant set of any vertex is a q-valent tree. We also give conditions on a rooted digraph Γ which allows us to construct a countable descendant-homogeneous digraph in which the descendant set of any vertex is isomorphic to Γ. © 2011 Elsevier B.V. All rights reserved.

Evans DM, Ferreira MS, 2012, The geometry of hrushovski constructions, ii. the strongly minimal case, *Journal of Symbolic Logic*, Vol: 77, Pages: 337-349, ISSN: 0022-4812

We investigate the isomorphism types of combinatorial geometries arising from Hrushovski's flat strongly minimal structures and answer some questions from Hrushovski's original paper. © 2012, Association for Symbolic Logic.

Evans DM, Ferreira MS, 2011, The geometry of Hrushovski constructions, I: The uncollapsed case, *Annals of Pure and Applied Logic*, Vol: 162, Pages: 474-488, ISSN: 0168-0072

An intermediate stage in Hrushovski's construction of flat strongly minimal structures in a relational language L produces ω-stable structures of rank ω. We analyze the pregeometries given by forking on the regular type of rank ω in these structures. We show that varying L can affect the (local) isomorphism type of the pregeometry, but not its finite subpregeometries. A sequel will compare these to the pregeometries of the strongly minimal structures. © 2011 Elsevier B.V.

Evans DM, Pastori E, 2011, Second cohomology groups and finite covers of infinite symmetric groups, *Journal of Algebra*, Vol: 330, Pages: 221-233, ISSN: 0021-8693

For Ω an infinite set, k≥2 and W the set of k-sets from Ω, there is a natural closed permutation group Γk which is a non-split extension 0→Z2W→Γk→Sym(Ω)→1. We classify the closed subgroups of Γk which project onto Sym(Ω). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms. © 2011 Elsevier Inc.

Evans DM, Wong MWHO, 2009, Some remarks on generic structures, *Journal of Symbolic Logic*, Vol: 74, Pages: 1143-1154, ISSN: 0022-4812

We show that the N0-categorical structures produced by Hrushovski's predimension construction with a control function fit neatly into Shelah's SOPn hierarchy: if they are not simple, then they have SOP3 and NSOP4. We also show that structures produced without using a control function can be undecidable and have SOP. © 2009, Association for Symbolic Logic.

Emms J, Evans DM, 2009, Constructing continuum many countable, primitive, unbalanced digraphs, *Discrete Mathematics*, Vol: 309, Pages: 4475-4480, ISSN: 0012-365X

We construct continuum many non-isomorphic countable digraphs which are highly arc transitive, have finite out-valency and infinite in-valency, and whose automorphism groups are primitive. © 2009 Elsevier B.V. All rights reserved.

Evans DM, 2008, Expansions of fields by angular functions, *Journal of the Institute of Mathematics of Jussieu*, Vol: 7, Pages: 735-750, ISSN: 1474-7480

The notion of an angular function has been introduced by Zilber as one possible way of connecting non-commutative geometry with two 'counterexamples' from model theory: the non-classical Zariski curves of Hrushovski and Zilber, and Poizat's field with green points. This article discusses some questions of Zilber relating to existentially closed structures in the class of algebraically closed fields with an angular function. © 2008 Cambridge University Press.

Evans DM, Hewitt PR, 2006, Continuous cohomology of permutation groups on profinite modules, *Communications in Algebra*, Vol: 34, Pages: 1251-1264, ISSN: 0092-7872

Model theorists have made use of low-dimensional continuous cohomology of infinite permutation groups on profinite modules, see Ahlbrandt and Ziegler (1991), Evans (1997b), Evans et al. (1997), and Hodges and Pillay (1994), for example. We expand the module category in order to widen the cohomological toolkit. For an important class of groups we use these tools to establish criteria for finiteness of cohomology.

Evans DM, 2005, Tivial stable structures with non-trivial reducts, *Journal of the London Mathematical Society*, Vol: 72, Pages: 351-363, ISSN: 0024-6107

A new viewpoint is offered on some of the generic structures constructed using Hrushovski's predimensions and it is shown that they are natural reducts of quite straightforward trivial, one-based stable structures. © 2005 London Mathematical Society.

Evans DM, 2004, Block transitive Steiner systems with more than one point orbit, *Journal of Combinatorial Designs*, Vol: 12, Pages: 459-465, ISSN: 1063-8539

For all 'reasonable' finite t; k, and s, we construct a t-(א0,k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2-(א0, 4, 1) design with a block-transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by-product of a new way of looking at a model-theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.

Evans DM, 2003, Ample dividing, *Journal of Symbolic Logic*, Vol: 68, Pages: 1385-1402, ISSN: 0022-4812

We construct a stable one-based, trivial theory with a reduct which is not trivial. This answers a question of John B. Goode. Using this, we construct a stable theory which is n-ample for all natural numbers n, and does not interpret an infinite group. © 2003, Association for Symbolic Logic. © 2003 Applied Probability Trust.

Evans DM, 2002, א<inf>0</inf>-categorical structures with a predimension, *Annals of Pure and Applied Logic*, Vol: 116, Pages: 157-186, ISSN: 0168-0072

We give an axiomatic framework for the non-modular simple א0-categorical structures constructed by Hrushovski. This allows us to verify some of their properties (weak elimination of imaginaries, simplicity, the nature of forking, CM-triviality and stable forking) in a uniform way, and to show that these properties are preserved by iterations of the construction. © 2002 Elsevier Science B.V. All rights reserved.

Evans DM, Rashwan OA, 2002, Bounds in the theory of finite covers, *Journal of Algebra*, Vol: 250, Pages: 757-777, ISSN: 0021-8693

We give an upper bound for the number of conjugacy classes of closed subgroups of the full wreath product FWrWSym(Ω) which project onto Sym(Ω). Here, Ω is infinite, W is the set of n-tuples of distinct elements from Ω (for some finite n), F is a finite nilpotent group, and the topology on the wreath product is that of pointwise convergence in its imprimitive permutation action. The result addresses a problem which arises in a natural model-theoretic context about classifying certain types of finite covers. © 2002 Elsevier Science (USA).

Evans DM, Pantano ME, 2002, א<inf>0</inf>-categorical structures with arbitrarily fast growth of algebraic closure, *Journal of Symbolic Logic*, Vol: 67, Pages: 897-909, ISSN: 0022-4812

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Evans DM, 2001, Suborbits in infinite primitive permutation groups, *Bulletin of the London Mathematical Society*, Vol: 33, Pages: 583-590, ISSN: 0024-6093

For every infinite cardinal κ. we construct a primitive permutation group which has a finite suborbit paired with a suborbit of size κ. This answers a question of Peter M. Neumann.

Brookes CJB, Evans DM, 2001, Augmentation modules for affine groups, *Mathematical Proceedings of the Cambridge Philosophical Society*, Vol: 130, Pages: 287-294, ISSN: 0305-0041

We prove that if k, F are fields of different characteristics then the permutation module kFn for the affine group AGL(n, F) has simple augmentation submodule. This proves a conjecture of A. R. Camina. © 2001 Cambridge Philosophical Society.

Evans DM, Wagner FO, 2000, Supersimple ω-categorical groups and theories, *Journal of Symbolic Logic*, Vol: 65, Pages: 767-776, ISSN: 0022-4812

An ω-categorical supersimple group is finite-by-abelian-by-finite, and has finite SU-rank. Every definable subgroup is commensurable with an acl(Ø)-definable subgroup. Every finitely based regular type in a CM-trivial ω-categorical simple theory is non-orthogonal to a type of SU-rank 1. In particular, a supersimple ω-categorical CM-trivial theory has finite SU-rank.

Evans DM, 1997, Finite covers with finite kernels, *Annals of Pure and Applied Logic*, Vol: 88, Pages: 109-147, ISSN: 0168-0072

We are concerned with the following problem. Suppose Γ and Σ are closed permutation groups on infinite sets C and W and ρ : Γ → Σ is a non-split, continuous epimorphism with finite kernel. Describe (for fixed Σ) the possibilities for ρ. Here, we consider the case where ρ arises from a finite cover π:C→W. We give reasonably general conditions on the permutation structure 〈W;Σ〉 which allow us to prove that these covers arise in two possible ways. The first way, reminiscent of covers of topological spaces, is as a covering of some Σ-invariant digraph on W. The second construction is less easy to describe, but produces the most familiar of these types of covers: a vector space covering its projective space.

Evans DM, 1997, Computation of first cohomology groups of finite covers, *Journal of Algebra*, Vol: 193, Pages: 214-238, ISSN: 0021-8693

We give several applications of standard methods of group cohomology to some problems arising in model theory concerning finite covers. We prove a conjecture of the author that for G-finite, א0-categorical structures the kernels of minimal superlinked finite covers have bounded rank. We show that the cohomology groups associated to finite covers of certain structures (amongst them, the primitive, countable, totally categorical structures) have to be finite. From this we deduce that the finite covers of these structures are determined up to finitely many possibilities by their kernels. © 1997 Academic Press.

Bryant RM, Evans DM, 1997, The small index property for free groups and relatively free groups, *Journal of the London Mathematical Society*, Vol: 55, Pages: 363-369, ISSN: 0024-6107

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