Leeds, UK ·
mmjtr
[at] leeds [dot] ac [dot] uk

I’m a Mathematics PhD student at the University of Leeds. I’m excited about research in higher category theory, topology and physics. I take particular interest in subjects that connect these three areas, like topological quantum field theories, the cobordism hypothesis and factorization homology. I also spend a lot of time thinking about models of (oo, n)-category and n-category for arbitrary finite n, as well as conversions between such models.

My current work centers around converting from ‘non-algebraic’ models of higher category to ‘algebraic ones’, along with the ramifications this has for modelling n-categorical TQFTs and comparing known constructions in the literature. I’m always excited to meet new people and hear about related ideas, so feel free to drop me a message if you want to chat!

November 2023

September 2020

September 2019

April 2019

September 2018

*Algebra Seminar, University of Leeds*

A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.

November 2023

*Quantum Maths Seminar, University of Nottingham*

A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.

November 2023

*Category Theory Octoberfest*

A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.

October 2023

*Manchester Category Theory Seminar, University of Manchester*

A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.

September 2023

*Yorkshire and Midlands Category Theory Seminar (YaMCATS), University of Cambridge*

Abstract: Across the multitude of definitions for a higher category, a dividing line can be found between two major camps of model. On one side lives the ‘algebraic’ models, like Bénabou’s bicategories, tricategories following Gurski and the models of Batanin and Leinster, Trimble and Penon. On the other end, one finds the ‘non-algebraic’ models, including those of Tamsamani and Paoli, along with quasicategories, Segal n-categories, complete n-fold Segal spaces and more. The bridges between these models remain somewhat mysterious. Progress has been made in certain instances, as seen in the work of Tamsamani, Leinster, Lack and Paoli, Cottrell, Campbell, Nikolaus and others. Nonetheless, the correspondence remains incomplete; indeed, for instance, there is no fully verified means in the literature to take an `algebraic’ homotopy n-category of any known model of (oo, n)-category for general $n$. In this talk, I will explore current work in the problem of taking homotopy bicategories of non-algebraic (oo, 2)-categories, including a construction of my own. If time permits, I will discuss some of the applications of this problem to topological quantum field theories.

September 2023

*Pure Postgraduate Research Seminar, University of Leeds*

An introduction to diffeological spaces, motivating them as an extension of smooth manifolds to a complete and cocomplete category.

March 2023

*Pure Postgraduate Research Seminar, University of Leeds*

A discussion of Milnor's exotic 7-sphere and exotic smooth structures in four dimensional manifolds.

November 2021

*Proofs, Constructions, Computations and Categories (PCCC) Seminar, University of Leeds*

A talk on Shulman's construction of a symmetric monoidal bicategory from a fibrant symmetric monoidal double category.

February 2022

*Proofs, Constructions, Computations and Categories (PCCC) Seminar, University of Leeds*

A talk presenting Batanin-Leinster style weak n-categories via globular operads.

October 2021

*Pure Postgraduate Research Seminar, University of Leeds*

An introductory talk on the correspondence between Kan complexes and weak homotopy types.

February 2021

*University of York*

An introductory course to simplicial and cell complexes, the fundamental group and the connections to group presentations therein.

June 2019

*University of York*

A presentation detailing my work on Turing Machine Networks.

April 2019

*University of York*

A short lecture series on code scheduling, including dependences and software pipelining.

June 2017

PhD in Mathematics

My PhD centers around higher category theory in topological quantum field theories. More precisely, I am developing a construction of the homotopy n-category of (oo, n)-categories to bridge the gap between these two sides of TQFT research. I am supervised by Joao Faria Martins, Paul Martin and (formerly) Nicola Gambino. I am funded by the Leeds Doctoral Scholarship.

2020 - 2023

MSc Mathematics and Foundations of Computer Science

I was a member of Lincoln College during my studies. My courses included Algebraic Topology, Algebraic Geometry, Category Theory, Scheme Theory, Lie Groups and Homological Algebra. I was a member of a reading group on higher category theory and wrote my dissertation on higher Artin stacks under Prof. Frances Kirwan.

2019 - 2020

BSc Computer Science and Mathematics (Year in Industry)

I finished a BSc in Computer Science and Mathematics at the University of York, receiving a First with Distinction and a mark of 90% overall. In this time, I received a prize for the highest results in the second year of the Computer Science department, the Cybula Prize for best finalist results in the Computer Science department, and the P. B. Kennedy Prize for Outstanding Achievement in the final degree examination in Mathematics. My year industry was completed at MIPS LLC.

2015 - 2019

International Baccalaureate

I received my IB Diploma at St. George's International School of Switzerland, earning a 40/45 overall. I ran a programming club and directed / was cast in several school plays during this time.

2013 - 2015

University of Leeds

Taught four problem classes for undergraduate students in the Department of Mathematics, on linear algebra and introductory geometry. Graded homework assignments for students with Gradescope.

October 2021 - December 2021

ThinCI

Developing demos and drivers for ThinCI's Graph Streaming Processor (GSP), an external chip for accelerated machine learning and computer vision processing.

June 2019 - September 2019

University of York

Worked alongside Graham Campbell and Detlef Plump with an EPSRC-funded summer grant to investigate an optimization for graph transformation-based programming languages, called 'root nodes'. Project was in the end successful, resulting in a report listed above. At the same time, worked with Ana Cavalcanti and Simon Foster on verification of reactive Circus processes; this did not result in a report due to time constraints.

June 2018 - September 2018

MIPS LLC.

Contributed to the MIPS Toolchain and GCC, in particular developing exception handling runtimes and interrupt code generation. Helped in development of new nanoMIPS ABI. Designed architecture for new OpenMP implementation for MIPS using MT ASE. Listed as a contributor to GCC nanoMIPS patch.

July 2017 - May 2018

Digital York

Worked alongside City of York Council to develop and teach a six-week introductory programming course to secondary school students. Course covered variables and types, control flow, data structures, functions, iteration vs recursion and example algorithms.

October 2016 - December 2016

University of York, Fulford School

Took part in the York Students In Schools volunteering programme to assist in several secondary school math classrooms for one term. Helped students with assignments and answered questions from students of all skill levels.

May 2016 - June 2016

August 2023

July 2023

Hausdorff Center for Mathematics, University of Bonn. (Homepage)

June 2023

Unviersity of Oxford. (Homepage)

June 2023

December 2022

July 2022

University of Copenhagen (attended online). (Homepage)

August 2021