Jack Romö
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!
Publications
Slides & Talks
Presentation - Homotopy Bicategories of Complete 2-fold Segal Spaces
Algebra Seminar, University of Leeds
A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.
Presentation - Constructing Homotopy Bicategories of Complete 2-fold Segal Spaces
Quantum Maths Seminar, University of Nottingham
A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.
Presentation - Constructing Homotopy Bicategories of Complete 2-fold Segal Spaces
Category Theory Octoberfest
A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.
Presentation - Constructing Homotopy Bicategories of Complete 2-fold Segal Spaces
Manchester Category Theory Seminar, University of Manchester
A talk on my construction of the homotopy bicategory of a complete 2-fold Segal space.
Presentation - Homotopy Bicategories of Complete 2-fold Segal Spaces
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.
Presentation - Diffeology: A Theory of Smoothness with Good Manners
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.
Presentation - Lovecraftian Geometry: An Introduction to Exotic Smooth Manifolds
Pure Postgraduate Research Seminar, University of Leeds
A discussion of Milnor's exotic 7-sphere and exotic smooth structures in four dimensional manifolds.
Presentation - Fantastic Symmetric Monoidal Bicategories and How to Construct Them
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.
Presentation - Defining n-Categories via Generalized Operads
Proofs, Constructions, Computations and Categories (PCCC) Seminar, University of Leeds
A talk presenting Batanin-Leinster style weak n-categories via globular operads.
Presentation - Simplicial Sets: The Convergence of Homotopy and Category Theory
Pure Postgraduate Research Seminar, University of Leeds
An introductory talk on the correspondence between Kan complexes and weak homotopy types.
Lecture Series - Introduction to Algebraic Topology
University of York
An introductory course to simplicial and cell complexes, the fundamental group and the connections to group presentations therein.
Presentation - Turing Machine Networks
University of York
A presentation detailing my work on Turing Machine Networks.
Lecture Series - Static Code Scheduling for Parallelism
University of York
A short lecture series on code scheduling, including dependences and software pipelining.
Education
University of Leeds
University of Oxford
University of York
St. George's International School of Switzerland
Experience
Teaching Assistant
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.
Graduate Design Engineer
Developing demos and drivers for ThinCI's Graph Streaming Processor (GSP), an external chip for accelerated machine learning and computer vision processing.
Undergraduate Researcher
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.
Toolchain Placement Engineer
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.
Coding Instructor
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.
Math Teaching Assistant
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.
Conferences Attended
Hausdorff School: TQFTs and Their Connections to Representation Theory and Mathematical Physics
Hausdorff Center for Mathematics, University of Bonn. (Homepage)
A Panorama of Homotopy Theory - a Conference in Honour of Mike Hopkins
Unviersity of Oxford. (Homepage)
Masterclass: Topological Field Theories and Factorization Homology
University of Copenhagen (attended online). (Homepage)