My primary research area is semigroup theory: I got interested in it as an undergraduate, its mixture of algebraic and combinatorial ideas was just right for my taste. Semigroups, being highly general algebraic structures, crop up virtually everywhere, and from early on in my work, I've been focusing on interactions with different areas of mathematics. I am particularly interested in inverse semigroups and their applications, with my main focus being étale groupoids and C*-algebras these days. I also have an interest in algorithmic problems in inverse semigroups, and in particular attacking these using ideas from geometric group theory. I recently organized a workshop on geometric semigroup theory, exploring the connections between semigroups and large scale geometry, and am organizing a conference on semigroups, groupoids and C*-algebras taking place in July 2024.
I enjoy collaborative work and (capacity allowing) keen to talk to, or work with people in similar or complementary research areas. I am also happy to consider supervising prospective PhD students – feel free to get in touch.
Geometric properties of inverse semigroups, Conference on Theoretical and Computational Algebra (Pocinho, Portugal, July 5, 2023)
Inverse semigroups as metric spaces, and their uniform Roe algebras, XVI Barcelona Weekend in Group Theory (Barcelona, Spain, May 5, 2023)
Inverse semigroups as metric spaces, and their uniform Roe algebras, An afternoon on group theory, ENS (Paris, France, Feb 22, 2023)
Inverse semigroups as metric spaces, and their uniform Roe algebras, NGGBT meeting (Manchester, UK, Dec 1, 2022)
The large scale geometry of inverse semigroups, ARTIN New Arrivals meeting (Edinbrugh, UK, May 31, 2022)
Proper and right subinvariant metrics on inverse semigroups, AMS 2022 Spring Western Sectional Meeting, Special Session on Recent Trends in Semigroup Theory (online, May 22, 2022)
Simplicity Nekrashevych algebras of contracting self-similar groups, British Early Career Mathematicians' Colloquium (online, June 15, 2021)
Simplicity of contracted inverse semigroup algebras, International Conference on Semigroups and Applications (Cochin, India, Dec 9, 2019)
Inverse monoids and immersions of cell complexes, NBSAN meeting (Manchester, UK, Jul 12, 2019)
Inverse monoids of partial graph automorphisms, International Conference on Semigroups 2018 (Lisbon, Portugal, July 12, 2018)
Inverse monoids and immersions of cell complexes, Rhodesfest81 (Ramat Gan, Israel, Jun 5, 2018)
Two examples of geometric methods in inverse semigroup theory, Winter One-relator Workshop (Norwich, UK, Jan 11, 2018)
On the graph condition regarding the F-inverse cover problem, AMS-EMS-SPM meeting, Algebraic Theory of Semigroups and Applications (Porto, Portugal, June 13, 2015)
Closure operators on group Cayley graphs, and presentations of F-inverse monoids, Panglobal Algebra and Logic Seminar, University of Colorado (online, Nov 14, 2023)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Functional Analysis seminar, University of Oxford (UK, June 6, 2023)
The large scale geometry of inverse semigroups, Geometry and Topology seminar, University of Bristol (UK, May 2, 2023)
Simplicity of Nekrashevych algebras of contracting self-similar groups, C*-algebras Oberseminar, University of Münster (Germany, Jan 10, 2023)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Analysis seminar, University of Glasgow (UK, Nov 24, 2022)
The large scale geometry of inverse semigroups, York Semigroup seminar, University of York (UK, Nov 2, 2022)
Inverse semigroups as metric spaces, and their uniform Roe algebras, Algebra seminar, University of Manchester, (UK, Nov 1, 2022)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Group Theory seminar, ICMAT, Madrid (Spain, May 6, 2022)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Pure Mathematics Colloquium, University of Manchester (UK, April 29, 2022)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Colloquium of the Mathematical Institute, Göttingen (online, Jan 14, 2021)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Western Sydney University Abend Seminars (online, Oct 22, 2020)
Simplicity of Nekrashevych algebras of contracting self-similar groups, Algebra seminar, Alfréd Rényi Institute of Mathematics, (online, Sept 28, 2020)
Simplicity of contracted inverse semigroup algebras, Algebra seminar, University of Szeged, (Hungary, Sept 2, 2020)
Simplicity of contracted inverse semigroup algebras, York Semigroup seminar, University of York, (online, May 20, 2020)
Hyperbolic and tree-like inverse monoids, York Semigroup seminar, University of York, (UK, Oct 17, 2019)
Algorithmic properties of tree-like inverse monoids, Algebra seminar, Heriot-Watt University, (Edinburgh, UK, May 22, 2019)
Algorithmic properties of tree-like inverse monoids, City University of New York, (USA, May 10, 2019)
Algorithmic properties of tree-like inverse monoids, Pure Mathematics Colloquium, University of St Andrews, (UK, Apr 4, 2019)
Inverse monoids and immersions of cell complexes, York Semigroup seminar, University of York, (UK, March 13, 2019)
Hyperbolic groups and generalizations I-II., Algebra Seminar, University of Szeged, (Hungary, March 14 & 21, 2018)
Inverse monoids and immersions of cell complexes, Algebra seminar, University of Porto, (Portugal, Nov 24, 2017)
Inverse monoids and immersions of cell complexes, NOVA University Lisbon, (Portugal, Nov 20, 2017)
Inverse monoids and immersions of cell complexes, University of Coimbra, (Portugal, Oct 17, 2017)
The algebraic structure of partial automorphisms of graphs, York Semigroup seminar, University of York, (UK, July 7, 2017)
The algebraic structure of partial automorphisms of graphs, Algebra seminar, Alfréd Rényi Institute of Mathematics, (Budapest, Hungary, May 8, 2017)
Inverse monoids and immersions of 2-complexes, Geometry seminar, Alfréd Rényi Institute of Mathematics, (Budapest, Hungary, Apr 25, 2014)
Inverse monoids and immersions of 2-complexes, Algebra seminar, University of Szeged, (Hungary, March 5, 2014)
F-inverse covers of inverse monoids, Groups, Semigroups and Topology seminar, University of Nebraska-Lincoln, (USA, Nov 5, 2013)
F-inverse covers of E-unitary inverse monoids, Algebra seminar, University of Szeged, (Hungary, Apr 17, 2013)