About

I am a Senior Research Associate in Mathematics at Lancaster University, working with Andrey Lazarev.

I used to be a postdoc at the University of Antwerp, working with Wendy Lowen and Dmitry Kaledin. Before that, I completed my PhD at the University of Edinburgh under the supervision of Jon Pridham, defending in 2019. My thesis was on a derived version of the Donovan-Wemyss contraction algebra. Before that, I obtained an MMath from the University of Oxford in 2015.

I am in a broad sense a noncommutative geometer; I am interested in anything that sits at the interfaces of algebraic geometry, homotopy theory, representation theory, and algebraic topology. I am particularly interested in:

• Deformation theory: Koszul duality, prorepresentability theorems, Mac Lane cohomology for abelian categories, topological Hochschild cohomology for ring spectra and spectral categories, noncommutative and derived deformations. Applications to algebraic topology.
• Derived noncommutative geometry: triangulated, dg, and spectral categories, noncommutative resolutions, contraction algebras and the homological MMP, singularity categories, matrix factorisations, Calabi--Yau algebras, links to representation theory.

Here is my CV, and here is my mathematical genealogy.

Contact

My office is Fylde College B44.
My email address is m dot booth4 at lancaster dot ac dot uk.
I have math.stackexchange and mathoverflow accounts, although I don't use them much.