Research

I am a mathematics researcher at the University of Lincoln, studying topological groups, and especially profinite groups. My current projects involve studying probabilistic finiteness conditions and probabilistic zeta functions for profinite groups, and studying the classification of totally disconnected, locally compact groups up to local isomorphism. I have previously constructed Eilenberg-MacLane spaces for totally disconnected groups, and investigated homological finiteness conditions for various classes of topological groups. I presented a poster on my zeta functions research in the UK Houses of Parliament in March 2023.

Qualifications

PhD in Mathematics, Royal Holloway, University of London (2016)
MMath, University of Cambridge (2012)
BA, University of Cambridge (2012)

Publications and preprints

Weil Zeta Functions of Group Representations over Finite Fields
with Steffen Kionke and Matteo Vannacci
Selecta Mathematica 30 (2024), 46.

Counting Irreducible Modules for Profinite Groups
with Steffen Kionke and Matteo Vannacci
Revista Matemática Iberoamericana 39 (2023), 4, 1519-1566.

Subgroups, hyperbolicity and cohomological dimension for totally disconnected locally compact groups
with Shivam Arora, Ilaria Castellano and Eduardo Martínez-Pedroza
Journal of Topology and Analysis 15 (2023), 1, 223-249.

Probabilistic Finiteness Properties for Profinite Groups
with Matteo Vannacci
Journal of Algebra 574 (2021), 584-616.

A Property of the Lamplighter Group
with Ilaria Castellano and Peter Kropholler
Topological Algebra and its Applications 8 (2020), 1, 1-4.

Finiteness Properties of Totally Disconnected Locally Compact Groups
with Ilaria Castellano
Journal of Algebra 543 (2020), 54-97.

Eilenberg-MacLane Spaces for Topological Groups
Axioms 8 (2019), 3, 90.

Homotopical algebra in categories with enough projectives
submitted; to appear.

On the Dimension of Classifying Spaces for Families of Abelian Subgroups
with Victor Moreno, Brita Nucinkis and Federico Pasini
Homology, Homotopy and Applications 19 (2017), 2, 83-87.

Continuous Cohomology and Homology of Profinite Groups
with Marco Boggi
Documenta Mathematica 21 (2016), 1269-1312.

On Profinite Groups of Type FP∞
Advances in Mathematics 294 (2016), 216-255.

Bieri-Eckmann Criteria for Profinite Groups
Israel Journal of Mathematics 212 (2016), 2, 857-893.