### David M Evans

Chair in Pure Mathematics, Department of Mathematics, Imperial College London, UK.

### Research

My research interests are in Model Theory: a branch of Mathematical Logic which has connections and interactions with a broad range of other areas of Mathematics. In my work the interactions are mainly with algebra and combinatorics and several of my papers could equally well be described as work on infinite permutation groups: studying the automorphism groups of algebraic and combinatorial structures using a mixture of model-theoretic and algebraic methods, or using model-theoretic constructions to produce infinite permutation groups and combinatorial structures with prescribed properties. Within model theory my interests are currently in stability theory and its generalizations, and Hrushovski constructions. Below, you can find a list of my papers and preprints, some lecture notes and slides of talks I have given, and a few other research-related things. Some of this is not very up-to-date; all of the formatting is very out-of-date.

The following list of papers is in approximate reverse chronological order. It contains links to some preprint versions of published papers (on Arxiv for recent papers), unpublished papers and papers in submission.

[57] Higher amalgamation properties in measured structures, Preprint, February 2022. Arxiv

[56] (with Jan Hubička, Matěj Konečný , Yibei Li and Martin Ziegler, Simplicity of automorphism groups of generalised metric spaces, J.Algebra 584 (2021), 163-179. Arxiv

[55] (with Jan Hubička, Matěj Konečný and Jaroslav Nešetřil) EPPA for two-graphs and antipodal metric spaces, Proc. American Math. Soc. 148 (2020), 1901-1915. Arxiv

[54] (with Jonathan Kirby and Tim Zander) Higher amalgamation properties in stable theories, Preprint, May 2018. Arxiv

[53] "Finite homogeneous geometries", Unpublished note, January 2017, Arxiv, 7pp.

[52] (with Thomas D. H. Coleman and Robert D. Gray) "Permutation monoids and MB-homogeneous structures", European J. Combinatorics 78 (2019), 163-189. Arxiv

[51] (with Jan Hubička and Jaroslav Nešetřil) "Automorphism groups and Ramsey properties of sparse graphs", Proc. London Math. Soc. (2019), https://doi.org/10.1112/plms.12238. Arxiv.

[50] (with Martin Bridson , Martin Liebeck and Dan Segal) "Algorithms determining finite simple images of finitely presented groups", Inventiones Mathematicae 218 (1019), 623-648. Arxiv.

[49] (with Jan Hubička and Jaroslav Nešetřil) "Ramsey properties and extending partial automorphisms for classes of finite structures'', Fundamenta Mathematicae 253 (2021), 121 - 153. Arxiv.

[48] (with Manuel Bodirsky, Michael Kompatscher and Michael Pinsker), "A counterexample to the reconstruction of omega-categorical structures from their endomorphism monoid", Israel J. Math. 224 (2018), 57-82. Arxiv

[47] (with Daniela Amato) "Infinite primitive and distance transitive directed graphs of finite out-valency", J. Combinatorial Theory, Series B, 114 (2015), pp. 33-50. (Open Access)

[46] (with Todor Tsankov) "Free actions of free groups on countable structures and property (T)", Fundamenta Mathematicae (2016) 232, 49-63. (ArXiv)

[45] (with Zaniar Ghadernezhad and Katrin Tent) "Simplicity of the automorphism groups of some Hrushovski constructions", Annals of Pure and Applied Logic 167 (2016), 22-48. (ArXiv)

[44] (with Daniela Amato and John K. Truss) "Classification of some countable descendant-homogeneous digraphs", Discrete Mathematics 312 (2012), pp. 911-919 (doi:10.1016/j.disc.2011.10.014). (ArXiv)

[43] "Matroid Theory and Hrushovski's Predimension Construction", Unpublished note, May 2011. (ArXiv)

[42] (with Marco Ferreira) "The geometry of Hrushovski constructions, II. The strongly minimal case", J. Symbolic Logic 77 (2012), pp. 337--349. (ArXiv)

[41] (with Marco Ferreira) "The geometry of Hrushovski constructions, I. The uncollapsed case", Annals of Pure and Applied Logic 162 (2011), pp. 474--488 (doi: 10.1016/j.apal.2011.01.008) (ArXiv)

[40] (with Elisabetta Pastori) "Second cohomology groups and finite covers of infinite symmetric groups", Journal of Algebra 330 (2011), 221--233 (doi:10.1016/j.jalgebra.2010.12.004). ArXiv

[39] (With Josephine Emms) "Constructing continuum many countable, primitive, unbalanced digraphs", Discrete Mathematics, 309 (2009), 4475-4480 (.pdf)

[38] "Expansions of fields by angular functions", J. Inst. Math. Jussieu (2008) 7 (4), 735--751. (.pdf)

[37] (with Mark Wing Ho Wong) "Some remarks on generic structures", J. Symbolic Logic (2009) 74 (4), 1143-1154. (.pdf)

[36] "Block transitive Steiner systems with more than one point orbit", J. Combinatorial Designs 12 (2004), 459-465. (.pdf)

[35] "Trivial stable structures with non-trivial reducts", J. London Math. Soc (2) 72 (2005), 351-363. (.pdf)

[34] (with Paul R. Hewitt) "Continuous cohomology of permutation groups on profinite modules", Communications in Algebra 34 (2006), 1251 - 1264. (.pdf)

[33] "Ample dividing", J. Symbolic Logic 68 (2003), 1385-1402. (.pdf) (There is a serious gap in this paper: see the slides from the 2013 Luminy talk below.)

[32] (with M. E. Pantano) "$\aleph_0$ categorical structures with arbitrarily fast growth of algebraic closure", J. Symbolic Logic 67 (2002), 897-909. (.dvi) (.ps)

[31] (with Osama A Rashwan) "Bounds in the theory of finite covers", Journal of Algebra 250 (2002), 757-777. (.ps) (.dvi)

[30] "Suborbits in infinite permutation groups", Bulletin London Math. Soc. 33 (2001), 583-590. (.dvi) (.ps)

[29] "$\aleph_0$-categorical structures with a predimension", Annals of Pure and Applied Logic 116 (2002), 157-186. (.dvi) (.ps)

[28] (with Frank O. Wagner) "Supersimple $\omega$-categorical groups and theories", J. Symbolic Logic, 65 (2000), 767-776. (.dvi) (.ps)

[27] (with C. J. B. Brookes) "Augmentation modules for affine groups", Math. Proc. Cambridge Phil. Soc. 130 (2001), 287-294. (.dvi) (.ps)

[26] (with D. G. D. Gray) "Kernels and cohomology groups for some finite covers", In Logic Colloquium '96, eds. J. M. Larrazabal, D. Lascar, G. Mints, Lecture Notes in Logic 12, pp 79-99, Springer Verlag, Berlin, 1998.

[25] Editor, Model Theory of Groups and Automorphism Groups. Proceedings of a Summer School in Blaubeuren, Germany, August 1995. London Mathematical Society Lecture Notes Series, 244, Cambridge University Press, 1997.

[24] "Finite covers of aleph zero categorical structures", in Advances in Model Theory and Algebra, eds. M. Droste and R. Goebel, Gordon and Breach (1997), 75-86.

[23] (with Alexandre A. Ivanov and Dugald Macpherson) "Finite Covers", in [25], 1-72.

[22] (with D. Lascar) "The automorphism group of the complex numbers is complete", in [25], 110-125.

[21] "Computation of first cohomology groups for some finite covers", Journal of Algebra (1997) 193, 214-238.

[20] (with Roger M. Bryant) "The small index property for free groups of countable rank", J. London Math. Soc. (2) 55 (1997), 363-369.

[19] "An infinite highly arc-transitive digraph", European J. Combinatorics 18 (1997), 281-286.

[18] "Finite covers with finite kernels", Annals of Pure and Applied Logic 88 (1997), 109-147.

[17] "Splitting of finite covers of $\aleph_0$-categorical structures", J. London Math. Soc. (2) 54 (1996), 210-226.

[16] (With Ehud Hrushovski) "The automorphism group of the combinatorial geometry of an algebraically closed field", Journal of the London Mathematical Society (2) 52 (1995), 209-225.

[15] "Examples of aleph-zero categorical structures", in 'Automorphisms of first-order structures', eds. R. Kaye & H.D. Macpherson, 33 - 72, Oxford University Press, Oxford 1994.

[14] "Some subdirect products of finite nilpotent groups", in Proceedings of the NATO ASI 'Finite and Infinite Combinatorics in Sets and Logic', Banff 1991, eds. N. Sauer, R. Woodrow, and B. Sands, NATO ASI Series C Volume 411, 117-124. Kluwer. Dordrecht 1993.

[13] (with Johannes Siemons) "The number of orbits of a group in two permutation representations", Archiv der Mathematik 60 (1993), 420 - 424.

[12] (with Ehud Hrushovski) "On the automorphism groups of finite covers", Annals of Pure and Applied Logic 62 (1993), 83 - 112.

[11] (With Wilfrid A. Hodges and Ian M. Hodkinson) "Automorphism groups of bounded abelian groups", Forum Mathematicum, 3 (1991), 523-541.

[10] (With A.Camina) "Some infinite permutation modules", Quarterly Journal of Mathematics (2) 42 (1991), 15-26.

[9] "The small index property for infinite dimensional classical groups", J. of Algebra. 136 (1991), 248-264.

[8] (With Ehud Hrushovski) "Projective planes in algebraically closed fields", Proc. London Math. Soc. (3) 62 (1991), 1-24.

[7] (With A.Pillay and B.Poizat) "Le groupe dans le groupe", Algebra i Logika 29 (1990), 368-378.

[6] (With Paul R. Hewitt) "Counterexamples to a conjecture on relative categoricity", Annals of Pure and Applied Logic 46 (1990), 201-209.

[5] "A note on automorphism groups of countably infinite structures",Archiv der Mathematik 49 (1987), 479-483.

[4] "Infinite permutation groups and minimal sets", Quarterly J. Math. (2) 38 (1987), 461-471.

[3] "Subgroups of small index in infinite general linear groups", Bull. London Math. Soc. 18 (1986), 587-590.

[2] "Homogeneous geometries", Proc. London Math. Soc. (3) 52 (1986), 305-327.

[1] "The 7-modular representations of Janko's smallest simple group", Journal of Algebra 96 (1985), 35-44.

#### Papers and theses by research students

[1] D. G. D. Gray, "The structure of some permutation modules for the symmetric group of infinite degree", Journal of Algebra 193 (1997), 122--143.

[2] Reinhold Konnerth, "Automorphism groups of differentially closed fields", Annals of Pure and Applied Logic 118 (2002), 1--60.

[3] Herwig Nuebling, "Adding Skolem functions to simple theories", Archive for Mathematical Logic 43 (2004), 359-370. (.pdf)

[4] Herwig Nuebling, "Reducts of stable, CM-trivial theories", J. Symbolic Logic 70 (2005), 1025-1036.

[5] Marco Antonio Semana Ferreira, "Geometries of Hrushovski Constructions", PhD Thesis, UEA, August 2009. (.pdf)

[6] Yibei Li, Normal subgroups of the automorphism groups of some homogeneous structures, PhD Thesis, Imperial College London, April 2021. https://doi.org/10.25560/89167

[7] Robert Sullivan, Aspects of the topological dynamics of sparse graph automorphism groups, PhD Thesis, Imperial College London, January 2022. https://doi.org/10.25560/95184

#### Slides from selected talks and some lecture notes

• "Model-theoretic constructions for omega-categorical structures", EURESCO meeting in Hattingen, July 2003. (.pdf)
• "Trivialising the Hrushovski constructions", Talk given at UEA, February 2004. (.pdf)
• "Expansions of fields by angular functions", Logicum Lugdunensis, June 2006. (.pdf)
• "Model-theoretic constructions via amalgamation and reducts", Notes on 4 talks given at the MATHLOGAPS Summer School, Aussois, France, June 2007. (.pdf) (There is a serious gap in these notes: see the slides from the 2013 Luminy talk below.)
• "Amalgamation constructions in permutation group theory and model theory", Talk at Peter Cameron's 60th birthday conference, Ambleside, August 2007. (.pdf)
• "Combinatorial geometries of the Hrushovski constructions", Talk at the Final Conference of MODNET, Barcelona, November 2008. (.pdf)
• "Finite Covers", ESF Conference on Model Theory, Bedlewo, Poland, August 2009. (.pdf)
• "Introduction to geometric stability theory", LMS-EPSRC Short Course on Model Theory, Leeds, July 2010. Notes etc.
• "Graphs, Matroids and the Hrushovski Construction", Algebra, Combinatorics and Model Theory, Istanbul, August 2011. (.pdf)
• "Geometric properties of forking in stable theories", CIRM, Luminy, May 2013. (.pdf)
• "Homogeneous structures, omega-categoricity and amalgamation constructions", talks given at the Hausdorff Institute for Mathematics, Bonn, September 2013. Notes
• "Automorphism groups of countable structures", talks given at Models and Groups 3, Istanbul, October 2014. Notes
• "An introduction to ampleness", talks given at British Postgraduate Model Theory Conference, Oxford, January 2015. Notes
• "Automorphism groups and Ramsey properties of sparse graphs", IHP, Paris, January 2018. Slides

#### Some reports on Grants

• Model theory of generic structures and simple theories (.pdf)
• Workshop on Pure Model Theory (.pdf)

This page maintained by David Evans, last updated, April 2022.