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Matthew Burke
Education

Macquarie University, Sydney
Doctor of Philosophy in Mathematics 2011-2015

Christ's College, University of Cambridge
Part III Mathematics (MMATH) 2010-2011
Bachelor's degree in Mathematics (BA) 2007-2010

Work experience

Cybera Data Science Fellowship
Aug 2019
Data science fellow


University of Calgary
Sep 2017-Present
Postdoctoral scholar


MathSpire Ltd.
Jun 2016-Aug 2017
Software engineer (5 months); Chief technology officer (9 months)


Debate Chamber Ltd.
Jul 2016-Aug 2016
Summer school tutor


Masaryk University, Brno
Oct 2015-Nov 2015
Visiting postdoctoral researcher


Macquarie University, Sydney
Jan 2012-Dec 2013
Tutor


Blue Tutors
Jun 2010
GCSE Tutor


Projects
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
Essay and thesis
Skills
LaTeX
  • Typesetting mathematics and mathematical diagrams for 3 papers in peer-reviewed mathematics journals.
  • Over 10 years of writing notes, technical reports and slide presentations.
F#
  • Over one year developing cross-platform desktop and mobile application using the .NET and Xamarin frameworks.
  • ASP.NET and WebSharper for web front-end 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
  • MiniMathJax (npm). A lightweight subset of MathJax that renders TeX using SVG.
  • Interoperation between F# and JavaScript in a WebView in Xamarin Forms.
  • Created interactive graphs using JSXGraph.
  • maths-inliner (npm). Finds formulas and replaces them with inline SVG images.
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
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
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]
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]
2019.05.31

Involution algebroids: a generalisation of Lie algebroids for tangent categories I
Foundational Methods in Computer Science

University of Calgary
2019.03.12

Involution algebroids and their homotopy theory II
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2019.03.05

Involution algebroids and their homotopy theory
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.12.03

Two dimensional Lie theory
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary [website]
2018.10.01

Introduction to univalence in Coq II
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary [website]
2018.09.24

Introduction to univalence in Coq
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.08.29

Linearisation of infinity categories
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.07.03

More Elements of the Theory of Quasi-categories
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.06.27

Elements of the Theory of Quasi-categories
Calgary Peripatetic Seminar in Logic and Category Theory

University of New Brunswick [website]
2018.06.04

The Calculus of Infinity Functors and Tangent Categories
Canadian Mathematical Society, Summer Meeting

Mount Allison University [website]
2018.06.02

Tangent Bundles of Groupoids, Pre-groupoids and Torsoids
26th Foundational Methods in Computer Science Workshop

University of Calgary
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
2018.04.30

A Two Dimensional Setting for the Calculus of Infinity Functors
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.03.26

Free co-completion, presheaves and sheaves
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.02.26

Localisation of Simplicial Presheaf Categories
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2018.01.22

The Calculus of Functors using Sheafification
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2017.10.13

Sites of Smooth Affine Schemes: Part III
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2017.10.06

Sites of Smooth Affine Schemes: Part II
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2017.09.22

Sites of Smooth Affine Schemes
Calgary Peripatetic Seminar in Logic and Category Theory

University of Calgary
2017.09.06

Lie's Third Theorem using an Intuitionistic Double Negation
Calgary Peripatetic Seminar in Logic and Category Theory

University of Cambridge [website]
2017.04.02

Lie's Third Theorem in Synthetic Differential Geometry [pdf]
Category Theory Seminar

University of Calgary
2016.10.07

Infinitesimals in Lie Theory [pdf]
Calgary Mathematics Department Colloquium

University of Calgary
2016.09.30

Lie Theory for Categories using Infinitesimals
Calgary Peripatetic Seminar in Logic and Category Theory

Universite Paris Diderot, Paris 7 [website]
2015.12.04

Multi-object Lie theory using synthetic differential geometry
Seminaire de geometrie et physique mathematique

University of Cambridge [website]
2015.11.17

A Synthetic Version of Lie's Second Theorem [pdf]
Category Theory Seminar

Masaryk University, Brno
2015.11.05

Lie's Second Theorem [pdf]
Algebra Seminar

Masaryk University, Brno
2015.10.28

Jet Part of a Category [pdf]
Algebra Seminar

Masaryk University, Brno
2015.10.26

An Introduction to Synthetic Differential Geometry [pdf]
Differential Geometry Seminar

Trest, Czech Republic [website]
2015.10.10

Synthetic Lie Theory [pdf]
Plenary Speaker at Eduard Cech Institute Workshop

Macquarie University [website]
2015.05.13ff

Jet Categories in the Cahiers Topos (2 talks)
Centre of Australian Category Theory

University of Cambridge [website]
2014.07.04

Synthetic Lie Theory [pdf]
Category Theory 2014

Macquarie University
2014.06.19

A Synthetic Perspective on the Integrability of Lie Algebroids
MCDC 2014

Macquarie University [website]
2014.05.21ff

A Synthetic Perspective on the Integrability of Lie Algebroids (3 talks)
Centre of Australian Category Theory

Macquarie University
2013.07.04

Cohomology from the Perspective of Restriction Categories and Atlases
MCDC 2013

Macquarie University
2012.06.15

Applications of Logic in Differential Geometry
MCDC 2012

University of Cambridge [website]
2011

Synthetic Differential Geometry
Part III talk