Matthew Burke
Education
Macquarie University, Sydney
Doctor of Philosophy in Mathematics 20112015
Christ's College, University of Cambridge
Part III Mathematics (MMATH) 20102011
Bachelor's degree in Mathematics (BA) 20072010
Work experience
Lyryx Learning Inc.
Jan 2020  present
Senior software developer
Cybera Data Science Fellowship
Aug 2019
Data science fellow
 Collaborated with an industry partner to clean, explore and analyse 7 years of live events data stored in a PostgreSQL database whose largest table had 13 million entries.
 Used Python scripts and Jupyter notebooks for data cleaning and exploration. Used the R programming language for data analysis and modelling.
 Used the plotly express visualisation library for histograms, scatter plots, box plots, choropleth maps etc.. Constructed a generalised linear model (GLM) for analysing count data and a log linear model for analysing sales data.
University of Calgary
Sep 2017Present
Postdoctoral scholar
 Designed and completed projects in pure mathematics and computer science leading to one publication in a peerreviewed journal and another submitted.
 Mentored two PhD students. Reviewed two papers for mathematics journals.
 Organised the University of Calgary Peripatetic Seminar (Dec 2017May 2019) and chaired a session of the Alberta Mathematics Dialogue 2018.
 Used Jupyter notebooks to lecture 4 classes of around 230 students each.
MathSpire Ltd.
Jun 2016Aug 2017
Software engineer (5 months); Chief technology officer (9 months)
 Developed a crossplatform mobile and desktop application to teach Alevel mathematics using interactive graphs, videos and integrated testing. Used F#, .NET and Xamarin.
 Created a web frontend and API for teachers to track student progress.
 Showcased application at the BETT education technology conference.
Debate Chamber Ltd.
Jul 2016Aug 2016
Summer school tutor
 Guided classes of around 14 Alevel students through university level material using a combination of presentations, exercises and group work.
Masaryk University, Brno
Oct 2015Nov 2015
Visiting postdoctoral researcher
 Plenary speaker at the multidisciplinary Eduard Cech Institute Workshop.
Macquarie University, Sydney
Jan 2012Dec 2013
Tutor
 Demonstrated solutions on the whiteboard for three undergraduate mathematics courses.
 Guided and motivated first year students at the dropin centre.
Blue Tutors
Jun 2010
GCSE Tutor
Projects

Kaggle Box Office Predictions: (https://github.com/mwpb/kaggleprojects)Competition to predict the revenue of films. Uses IPython and Google Colab.

Cryptopals challenges: (https://github.com/mwpb/matasanogo)Solutions written in Go. Work in progress: currently first three sets completed.

Colimits in Coq: (https://github.com/mwpb/postulatedcolimitsincoq)Computer verification of a key result in category theory using the Coq proof assistant.

ChessLogBook: (https://mwpb.uk/ChessLogBook)MacOS app written using Qt to play games on freechess.org and annotate them offline.
Professional development and prizes
 2018
 Mitacs online workshop: Managing Project Timelines
 2016
 University of Michigan on Coursera: Using Python to Access Web Data
 2016
 University of Michigan on Coursera: Using Databases with Python
 2008
 Christ's College Whelan Prize for First Class Examination Performance
Research papers
 Involution algebroids: a generalisation of Lie algebroids for tangent categories, Submitted to Advances in Mathematics. Joint with Benjamin MacAdam. Available at arXiv.
 A Synthetic Version of Lie’s Second Theorem, Applied Categorical Structures , 2018.02.06. Available at arXiv and publisher.
 Connected Lie Groupoids are Internally Connected and Integral Complete in Synthetic Differential Geometry, Symmetry, Integrability and Geometry: Methods and Applications, 2016.06.29. Available at arXiv and publisher.
Essay and thesis
Skills
 LaTeX

 Typesetting mathematics and mathematical diagrams for 3 papers in peerreviewed mathematics journals.
 Over 10 years of writing notes, technical reports and slide presentations.
 F#

 Over one year developing crossplatform desktop and mobile application using the .NET and Xamarin frameworks.
 ASP.NET and WebSharper for web frontend and web API.
 C#

 Over one year using and creating bug reports for open source software on GitHub.
 SQL and NoSQL

 2016: University of Michigan on Coursera: Using Databases with Python
 Accessing SQL Server database using both F# type providers, Entity Framework and raw SQL queries.
 Google Firestore NoSQL Database
 HTML, CSS and JavaScript
 Python and Jupyter notebook

 Kaggle Box Office Predictions Competition above.
 Jupyter notebooks used in MATH211 lectures at the University of Calgary.
 ChessLogBook native application above.
 Coq proof assistant

 Computer verification of result that monomorphisms are closed under pushout in a Grothendieck topos.
 Series of seminar talks about formulating HoTT in the Coq proof assistant.
Talks
University of Calgary
Lie algebroids are the same as involution algebroids in the category of smooth manifolds
Calgary Peripatetic Seminar in Logic and Category Theory
2019.11.01
Lie algebroids are the same as involution algebroids in the category of smooth manifolds
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Differential bundles in the category of smooth manifolds
Calgary Peripatetic Seminar in Logic and Category Theory
2019.09.06
Differential bundles in the category of smooth manifolds
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary, Kananaskis Field Station [website]
Involution algebroids: a generalisation of Lie algebroids for tangent categories II
Foundational Methods in Computer Science
2019.05.31
Involution algebroids: a generalisation of Lie algebroids for tangent categories II
Foundational Methods in Computer Science
University of Calgary, Kananaskis Field Station [website]
Involution algebroids: a generalisation of Lie algebroids for tangent categories I
Foundational Methods in Computer Science
2019.05.31
Involution algebroids: a generalisation of Lie algebroids for tangent categories I
Foundational Methods in Computer Science
University of Calgary
Involution algebroids and their homotopy theory II
Calgary Peripatetic Seminar in Logic and Category Theory
2019.03.12
Involution algebroids and their homotopy theory II
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Involution algebroids and their homotopy theory
Calgary Peripatetic Seminar in Logic and Category Theory
2019.03.05
Involution algebroids and their homotopy theory
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Two dimensional Lie theory
Calgary Peripatetic Seminar in Logic and Category Theory
2018.12.03
Two dimensional Lie theory
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary [website]
Introduction to univalence in Coq II
Calgary Peripatetic Seminar in Logic and Category Theory
2018.10.01
Introduction to univalence in Coq II
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary [website]
Introduction to univalence in Coq
Calgary Peripatetic Seminar in Logic and Category Theory
2018.09.24
Introduction to univalence in Coq
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Linearisation of infinity categories
Calgary Peripatetic Seminar in Logic and Category Theory
2018.08.29
Linearisation of infinity categories
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
More Elements of the Theory of Quasicategories
Calgary Peripatetic Seminar in Logic and Category Theory
2018.07.03
More Elements of the Theory of Quasicategories
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Elements of the Theory of Quasicategories
Calgary Peripatetic Seminar in Logic and Category Theory
2018.06.27
Elements of the Theory of Quasicategories
Calgary Peripatetic Seminar in Logic and Category Theory
University of New Brunswick [website]
The Calculus of Infinity Functors and Tangent Categories
Canadian Mathematical Society, Summer Meeting
2018.06.04
The Calculus of Infinity Functors and Tangent Categories
Canadian Mathematical Society, Summer Meeting
Mount Allison University [website]
Tangent Bundles of Groupoids, Pregroupoids and Torsoids
26th Foundational Methods in Computer Science Workshop
2018.06.02
Tangent Bundles of Groupoids, Pregroupoids and Torsoids
26th Foundational Methods in Computer Science Workshop
University of Calgary
A Two Dimensional Setting for the Calculus of Infinity Functors: Part II
Calgary Peripatetic Seminar in Logic and Category Theory
2018.05.14
A Two Dimensional Setting for the Calculus of Infinity Functors: Part II
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
A Two Dimensional Setting for the Calculus of Infinity Functors
Calgary Peripatetic Seminar in Logic and Category Theory
2018.04.30
A Two Dimensional Setting for the Calculus of Infinity Functors
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Free cocompletion, presheaves and sheaves
Calgary Peripatetic Seminar in Logic and Category Theory
2018.03.26
Free cocompletion, presheaves and sheaves
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Localisation of Simplicial Presheaf Categories
Calgary Peripatetic Seminar in Logic and Category Theory
2018.02.26
Localisation of Simplicial Presheaf Categories
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
The Calculus of Functors using Sheafification
Calgary Peripatetic Seminar in Logic and Category Theory
2018.01.22
The Calculus of Functors using Sheafification
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Sites of Smooth Affine Schemes: Part III
Calgary Peripatetic Seminar in Logic and Category Theory
2017.10.13
Sites of Smooth Affine Schemes: Part III
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Sites of Smooth Affine Schemes: Part II
Calgary Peripatetic Seminar in Logic and Category Theory
2017.10.06
Sites of Smooth Affine Schemes: Part II
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Sites of Smooth Affine Schemes
Calgary Peripatetic Seminar in Logic and Category Theory
2017.09.22
Sites of Smooth Affine Schemes
Calgary Peripatetic Seminar in Logic and Category Theory
University of Calgary
Lie's Third Theorem using an Intuitionistic Double Negation
Calgary Peripatetic Seminar in Logic and Category Theory
2017.09.06
Lie's Third Theorem using an Intuitionistic Double Negation
Calgary Peripatetic Seminar in Logic and Category Theory
University of Cambridge [website]
Lie's Third Theorem in Synthetic Differential Geometry [pdf]
Category Theory Seminar
2017.04.02
Lie's Third Theorem in Synthetic Differential Geometry [pdf]
Category Theory Seminar
University of Calgary
Infinitesimals in Lie Theory [pdf]
Calgary Mathematics Department Colloquium
2016.10.07
Infinitesimals in Lie Theory [pdf]
Calgary Mathematics Department Colloquium
University of Calgary
Lie Theory for Categories using Infinitesimals
Calgary Peripatetic Seminar in Logic and Category Theory
2016.09.30
Lie Theory for Categories using Infinitesimals
Calgary Peripatetic Seminar in Logic and Category Theory
Universite Paris Diderot, Paris 7 [website]
Multiobject Lie theory using synthetic differential geometry
Seminaire de geometrie et physique mathematique
2015.12.04
Multiobject Lie theory using synthetic differential geometry
Seminaire de geometrie et physique mathematique
University of Cambridge [website]
A Synthetic Version of Lie's Second Theorem [pdf]
Category Theory Seminar
2015.11.17
A Synthetic Version of Lie's Second Theorem [pdf]
Category Theory Seminar
Masaryk University, Brno
An Introduction to Synthetic Differential Geometry [pdf]
Differential Geometry Seminar
2015.10.26
An Introduction to Synthetic Differential Geometry [pdf]
Differential Geometry Seminar
Trest, Czech Republic [website]
Synthetic Lie Theory [pdf]
Plenary Speaker at Eduard Cech Institute Workshop
2015.10.10
Synthetic Lie Theory [pdf]
Plenary Speaker at Eduard Cech Institute Workshop
Macquarie University [website]
Jet Categories in the Cahiers Topos (2 talks)
Centre of Australian Category Theory
2015.05.13ff
Jet Categories in the Cahiers Topos (2 talks)
Centre of Australian Category Theory
Macquarie University
A Synthetic Perspective on the Integrability of Lie Algebroids
MCDC 2014
2014.06.19
A Synthetic Perspective on the Integrability of Lie Algebroids
MCDC 2014
Macquarie University [website]
A Synthetic Perspective on the Integrability of Lie Algebroids (3 talks)
Centre of Australian Category Theory
2014.05.21ff
A Synthetic Perspective on the Integrability of Lie Algebroids (3 talks)
Centre of Australian Category Theory
Macquarie University
Cohomology from the Perspective of Restriction Categories and Atlases
MCDC 2013
2013.07.04
Cohomology from the Perspective of Restriction Categories and Atlases
MCDC 2013
Macquarie University
Applications of Logic in Differential Geometry
MCDC 2012
2012.06.15
Applications of Logic in Differential Geometry
MCDC 2012