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; my research interests sit at the interface 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.
- Derived noncommutative geometry: triangulated, dg, and spectral categories, noncommutative resolutions, contraction algebras and the homological MMP, singularity categories, matrix factorisations, links to representation theory.
Here is my CV, and here is my mathematical genealogy.
My office is Fylde College B31.
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.