Jonathan

Noel

Assistant Professor in the Department of Mathematics and Statistics at the University of Victoria in the Discrete Mathematics Group.

Research Interests

- Extremal combinatorics
- Analytic limits of combinatorial objects
- Quasirandomness
- Probability theory
- Ramsey theory
- Graph colourings and homomorphisms
- Percolation
- Algorithms and complexity
- Descriptive combinatorics

Five Selected Publications

- Circle Squaring with Pieces of Small Boundary and Low Borel Complexity
- joint with András Máthé and Oleg Pikhurko. Submitted
- Quanta Magazine article
- Popular Mechanics article
- Discover Magazine article

- Six Permutation Patterns Force Quasirandomness
- joint with Gabriel Crudele and Peter J. Dukes. Accepted to Discrete Analysis.

- Extremal Bounds for Bootstrap Percolation in the Hypercube
- joint with Natasha Morrison. J. Combin. Theory Ser. A 156 (2018) 61–84.

- Weak regularity and finitely forcible graph limits
- joint with Jacob W. Cooper, Tomáš Kaiser and Daniel Kráľ. Trans. Amer. Math. Soc. 370 (6) (2018) 3833–3864.
- Cited in Lovász’s 2021 Abel Prize Lecture

- A Proof of a Conjecture of Ohba
- joint with Bruce A. Reed and Hehui Wu. J. Graph Theory 79 (2) (2015) 86–102.
- One of the problems popularized in the 2008 book Graph Theory by Bondy and Murty.

Education and CV

University of Oxford

Defended: June 2016

DPhil Thesis: Extremal Combinatorics, Graph Limits and Computational Complexity

Adviser: Alex Scott

McGill University

April 2013

Masters Thesis: Choosability of Graphs with Bounded Order: Ohba's Conjecture and Beyond

Adviser: Bruce Reed

Thompson Rivers University

April 2011

Honours Thesis: The Invariant Subspace Problem

Adviser: Robb Fry

Service and Outreach

I am a co-organizer for the Discrete Math Seminar at UVic with Joseph Hyde and Natasha Morrison

I am on the Executive Committee of the Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM).

I am on the Program Committee of CanaDAM 2025 taking place in Ottawa on May 26-29, 2025

Here is a video from April 2024 of two of my grad students and I giving an overview of the Szemerédi Regularity Lemma

Here is a talk that I gave at the 2024 AMS Spring Western Sectional Meeting: slides

I organized a Minisymposium on Extremal Combinatorics and Beyond at CanaDAM 2023.

In November 2022, I gave an outreach talk Solving HUGE Problems Quickly in the IMAGINING UVic: Inspiring Mathematical Growth and Intuition in Girls seminar series. Slides.

In 2022, Donga Science (Korea) made a comic for children based on my paper with Oleg Pikhurko and András Máthé on Tarski’s Circle Squaring Problem. Here is a pdf of the comic.

I was on the Program Committee for the 2022 ACM-SIAM Symposium on Discrete Algorithms (SODA22)

I co-organized a Minisymposium on Bootstrap Percolation at CanaDAM 2019 with Natasha Morrison.

I was on the Program Committee for the 2019 Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2019).

I am an active contributor of AMS Mathematical Reviews.

NSERC Grant

NSERC Discovery Grant: Large Combinatorial Objects: Extremal Structure and Quasirandomness

Students and Postdocs

We are always looking for Undergraduate, Master's and PhD students and Postdoctoral Researchers to join our group. My work focuses on problems in extremal and probabilistic combinatorics using methods from other areas such as analysis, algebra, computer science and optimization. No prior experience in these areas is required. If this sounds exciting to you, then do not hesitate to send me an e-mail at noelj@uvic.ca!

Postdocs:

Current:

2. Joseph Hyde. University of Victoria, Started in August 2022. Co-supervised with Natasha Morrison and Bruce Reed.

Past:

1. Natalie Behague. University of Victoria, January 2022 to November 2023. Co-supervised with Natasha Morrison. Now a postdoc at the University of Warwick.

PhD Students:

Current:

1. Jae-baek Lee. University of Victoria, Started in January 2021. Co-supervised with Gary MacGillivray.

Master's Students:

Current:

5. Lina Maria Simbaqueba Marin. University of Victoria, Started in September 2023.

4. Ashna Wright. University of Victoria, Started in September 2022. Co-supervised with Natasha Morrison.

Past:

3. Arjun Ranganathan, Inducing Graphs, Hypergraphs, and Tournaments. IISER, Pune, 2023-2024. Co-supervised with Matthew Kwan. Soon to be a PhD student at University College London.

2. Abel Romer, Tight Bounds on 3-Neighbor Bootstrap Percolation. University of Victoria, 2020-2022. Co-supervised with Peter Dukes.

1. Vincent Pfenninger, Graph Bootstrap Processes in Complete Bipartite Graphs. ETH Zürich, Spring Semester 2017. Co-supervised with Benny Sudakov. Now a postdoc at TU Graz.

Undergraduate Research Students:

Current:

7. Christopher Turton. University of Victoria, NSERC USRA Summer Research Student. May-Aug 2024.

Past:

6. Elena Moss. University of Victoria, NSERC USRA Summer Research Student. May-Aug 2023. Now a Graduate Student at the Berlin Mathematical School. See also this article on Elena‘s mathematical journey.

5. Gabriel Crudele, Six Permutation Patterns Force Quasirandomness. University of Victoria, Summer Research Student, May-Aug 2022. Co-supervised with Peter Dukes. Now a Master's Student at McGill University.

4. Elena Moss, Off-Diagonal Ramsey Multiplicity. University of Victoria, NSERC USRA Summer Research Student, May-Aug 2022. Now a Graduate Student at the Berlin Mathematical School. See also this article on Elena‘s mathematical journey.

3. Lina Maria Simbaqueba Marin, Sidorenko-Type Inequalityies for Pairs of Trees. University of Victoria, Mitacs Globalink Research Intern from Universidad Nacional de Colombia, May-Aug 2022. Now a Master's Student at the University of Victoria.

2. Arjun Ranganathan, On the Running Time of Hypergraph Bootstrap Percolation. Research Intern from IISER, Pune, June 2021-May 2022.

1. Joe Wall, Saturation and Weak Saturation. University of Warwick, URSS Program, Summer 2018. Now a PhD student at Lancaster University.

Undergraduate Theses:

Current:

None

Past:

6. Gabriel Crudele. University of Victoria. 2022/2023. Now a Master's Student at McGill University.

5. Adam Finchett. Graph Limits, Norms and Applications. 4th Year Essay. University of Warwick, 2019/2020. Now a Data Scientist at Schroders Personal Wealth.

4. Matt Pike. Problems in Bootstrap Percolation. 4th Year Essay. University of Warwick, 2018/2019.

3. Rachel Hardgrave. Classical Theorems in List Colouring. 3rd Year Essay. University of Warwick, 2019/2020.

2. Sophia Werner. Semi-Definite Programming. 3rd Year Essay. University of Warwick, 2018/2019.

1. Stefan Lochau. Entropy and Linear Programming Methods for Counting Matchings and Independent Sets in Graphs. Bachelor Thesis. ETH Zürich, Autumn Semester 2016. Co-supervised with Benny Sudakov. Now a software engineer at M&F Engineering AG.

Applying to UVic for Master's or PhD

If you would like to apply to be a grad student at UVic, please take note of the deadlines. Applications sometimes take weeks or months to go through the UVic internal system before profs can see them. A surprisingly high percentage of applications to our department arrive so late that professors do not even see them until after they have made their decisions on graduate students (if at all). This is especially true for international students. I would therefore recommend applying as early as possible, preferably weeks or even months before the deadline. After submitting your application through the UVic system, I would recommend also sending it to your potential supervisor(s) directly. This is the only way that you can assume that they have had a chance to see your application!

Before applying to UVic, you should familiarize yourself with our program. One source of information is the Graduate Handbook. It should give you a rough idea of what to expect and you can get in touch with me for further information.

All PhD students in our department have to pass something called “candidacy,” which is supposed to take place before they start doing research. However, if you come to do a PhD with me, then we will start doing research as soon as you are ready (which may be before you have completed candidacy; perhaps even the first day of your PhD). I will do my best to come up with a candidacy plan that helps you move towards your future goals as effectively as possible (subject to the approval of the department), whatever those goals may be.

Advice for Early Career Researchers

General Advice:

— Gian-Carlo Rota's Ten Lessons I Wish I Had Been Taught.

— Advice to a Young Mathematician with contributions from Sir Michael Atiyah, Béla Bollobás, Alain Connes, Dusa McDuff, and Peter Sarnak.

— Terence Tao's Career Advice.

— Fan Chung's Advice for grad students.

— William P. Thurston's On Proof and Progress in Mathematics.

— Guidance for graduate students, new PhDs, and professionals at all levels from the Committee on the Status of Women in Computing Research.

— Specific information for math grad students at UVic can be found on the Guidelines page on the UVic Math & Stats Department site. In particular, I suggest reading the graduate handbook.

Writing and Presenting Mathematics:

— Paul Halmos' How to Write Mathematics and How to Talk Mathematics.

— Donald E. Knuth, Tracy Larrabee and Paul M. Roberts' Mathematical Writing.

— Keith Conrad's Advice on Mathematical Writing.

— Stephen G. Krantz's How to Write Your First Paper.

— John Etnyre's The Art of Writing Introductions.

— Francis Su's Guidelines for Good Mathematical Writing.

— Agelos Georgakopoulos' webpage on How to Give a Good Talk.

— Bruce C. Berndt's How to Write Mathematical Papers.

— Chris Godsil's Advice on how to write well and give good talks.

— Doug West's The Grammar According to West.

— Terence Tao's On Writing.

— Tim Gowers' How should mathematics be taught to non-mathematicians?

Other Advice:

• Familiarize yourself with the types of questions that one is asked during a PhD, postdoc or faculty position interview and practice answering them. I have started to compile a list of possible interview questions for jobs in mathematics that you may find helpful.

• I recommend all students and early career researchers in discrete mathematics to subscribe to the Discrete Mathematics and Algorithms Network (DMANET) mailing list. This will provide information on opportunities (jobs, scholarships, events, etc) in the area.

• I also recommend subscribing to the math.CO arxiv mailing list to keep yourself up to date on the latest developments in the area.

• It is important for early career researchers to have an academic webpage. This still applies if you have only a few papers, or none at all. It is crucial that people can easily find out (a) who you are, (b) where you are, (c) what you're interested in, and (d) what you've done. You don't want to miss out on opportunities just because people can't find you!

• Go to conferences and give talks. Its a great way to meet new people in the area, get exposure to new ideas and disseminate your work. Doug West maintains a comprehensive list of conferences in combinatorics.

Equity, Diversity and Inclusion

Members of underrepresented groups face special obstacles in the mathematical sciences, and in academia more broadly. Mathematics, and academia as a whole, is still in the process of understanding and recognizing these challenges and learning how to overcome them, but some great progress is being made by some amazing people. For more information:

— The Math is For All project created by Annie Raymond; see also the Instagram.

— Lathisms: Latinxs and Hispanics in the Mathematical Sciences.

— Indigenous Mathematicians webpage.

— Mathematically Gifted and Black webpage.

— National Association of Mathematicians promotes mathematics in underrepresented minorities

— Mathematicians of the African Diaspora webpage.

— Meet a Mathematician shares stories of mathematicians from diverse backgrounds.

— the Association for Women in Mathematics UVic Student Chapter.

— UVic's Policy on Human Rights, Equity and Fairness.

— The webpage for the Math & Statistics Equity, Diversity and Inclusion (MSEDI) committee at UVic.

— NSERC's Guide for Applicants: Considering equity, diversity and inclusion in your application.

— LMS Advice on Diversity at Conferences and Seminars.

— The Women in Combinatorics (WinCom) group maintains a database of female researchers. This is a valuable resource. E.g., event organizers can use it to improve diversity among invited speakers.

Funding and Jobs

Undergraduate Research

• NSERC Undergraduate Student Research Awards (USRA); see also the Math & Stats webpage

• UVic Science Undergraduate Research Awards (SURA); see also the Math & Stats webpage

• UVic Jamie Cassels Undergraduate Research Awards (JCURA); see also the Math & Stats webpage

• UVic Valerie Kuehne Undergraduate Research Awards (VKURA); see also the Math & Stats webpage

• The Mitacs Globalink Research Awards provide funding for senior undergraduates, graduate students and postdocs to undertake a 12- to 24-week research project in another country.

Undergraduate Travel Funding

• UVic Boehm Family Award for Undergraduate Travel

International Undergraduate Research Internships

• Mitacs Globalink Research Internship

Undergraduate Activities

• Canadian Mathematics Society Student Committee Student Activities Funding Application

Graduate Student Funding (Master's and PhD)

• NSERC Postgraduate Scholarships and Canada Graduate Scholarships (PGS/CGS M and D) (Canadian citizens and permanent residents only)

• NSERC Vanier Canada Graduate Scholarships

• Mitacs Globalink Graduate Fellowship (only for former Mitacs Globalink Interns)

• More information about funding opportunities for grad students can be found on the UVic Math & Stats Financial Support page

Graduate Student Travel Funding (Master's and PhD)

• The Faculty of Graduate Studies at UVic offers Travel Grants

• CUPE 4163 offers Conference Funding for TAs and other members.

• The Mitacs Globalink Research Awards provide funding for senior undergraduates, graduate students and postdocs to undertake a 12- to 24-week research project in another country.

• Many conferences offer travel funding for students. For students in combinatorics, the SIAM Discrete Math Conference (held in even years) and the CanaDAM Conference (held in odd years) usually do. If you want to get travel funding, then you should probably plan to present a talk.

Postdoctoral Fellowships

• Pacific Institute for the Mathematical Sciences (PIMS) Postdoctoral Fellowships

• Centre de recherches mathématiques (CRM) Postdoctoral Fellowships

• Fields Research Fellowships

• NSERC Postdoctoral Fellowships

• NSERC Banting Postdoctoral Fellowships

• PIMS/CNRS Postdoctoral Fellowships are for researchers who are French or completed their PhD in France to work in Canada

• European Research Council (ERC) Marie Skłodowska-Curie Fellowships are postdoctoral positions to be held in the EU, or for EU researchers

• Leverhulme Early Career Fellowships are postdoctoral positions to be held in the UK

• The Royal Society University Research Fellowships are highly competitive independent postdoctoral positions to be held in the UK

• Heilbronn Research Fellowships are postdoctoral positions in mathematics that can be held at several universities in the UK (but primarily at the University of Bristol).

• Humboldt Postdoctoral Research Fellowships are postdoctoral positions to be held in Germany.

• Warwick Zeeman Lecturer is an independent postdoctoral position at the University of Warwick

• Junior Research Fellowships are highly competitive independent postdoctoral positions offered by colleges at the University of Cambridge and the University of Oxford. Some of them are posted here and here and others can be found by searching through the webpage of the individual college or jobs.ac.uk.

• Imperial College Research Fellowships are highly competitive independent postdoctoral positions

• Dirichlet Postdoctoral Fellowships are independent postdoctoral positions offered by the Berlin Mathematical School.

• Many mathematics jobs, mostly in the USA and Canada, can be found at mathjobs.org

• Many academic jobs, mostly in the UK, can be found at jobs.ac.uk

• Many mathematics jobs, mostly in Europe, can be found on the European Mathematical Society website

• Mathematical jobs within or outside of academia can be found at Mathhire.org

• A great resource for finding mathematics jobs, mostly in the USA, is the AWM Job Board

Postdoc Travel Funding

• The Mitacs Globalink Research Awards provide funding for senior undergraduates, graduate students and postdocs to undertake a 12- to 24-week research project in another country.

• Many conferences offer travel funding for students. For students in combinatorics, the SIAM Discrete Math Conference (held in even years) and the CanaDAM Conference (held in odd years) usually do. If you want to get travel funding, then you should probably plan to present a talk.

Teaching

CURRENT TEACHING

None

FUTURE TEACHING

First Term, 2024/2025:

• Lecturer for Math 122: Logic and Foundations (Sections A03 and A04).

• Course Coordinator for Math 122: Logic and Foundations.

• Lecturer for Math 426/529: Extremal Combinatorics. Here is the webpage for the course. It is also being offered as a PIMS Network Wide Graduate Course. Anyone who would like to participate in the course remotely through Zoom can do so. Please e-mail me and I will send you the Zoom link.

PAST TEACHING

University of Victoria

Second Term, 2023/2024:

• Lecturer for Math 498: Seminar and Independent Project.

First Term, 2023/2024:

• Lecturer for Math 151: Finite Mathematics (Sections A01 and A02). Here is a schedule of the lectures for Section A01 and Section A02.

• Course Coordinator for Math 151: Finite Mathematics.

• Lecturer for Math 498: Seminar and Independent Project.

First Term, 2022/2023:

• Lecturer for Math 122: Logic and Foundations (Sections A03 and A04). Here is a schedule of the lectures for Section A03 and Section A04. Here is a YouTube playlist of the lecture videos from the 2021/2022 academic year.

• Lecturer for Math 492/529: Topics in Applied Mathematics/Discrete Mathematics (Extremal Combinatorics). Here is a schedule of the lectures and a link to the course notes. Here is a YouTube Playlist of the lecture videos from the 2020/2021 academic year. Now known as Math 426.

First Term, 2021/2022:

• Lecturer for Math 122: Logic and Foundations (Section A01 and Section A03). Here is a schedule of the lectures for Section A01 and Section A03. Here is a YouTube playlist of the lecture videos.

• Lecturer for Math 222: Discrete and Combinatorial Mathematics. Here is a schedule for the course.

Second Term, 2020/2021:

• Lecturer for Math 492/529: Topics in Applied Mathematics/Discrete Mathematics (Extremal Combinatorics). Here is a schedule of the lectures. Here is a YouTube Playlist of the lectures. Now known as Math 426.

• Lecturer for Math 222: Discrete and Combinatorial Mathematics. Here is a schedule of the lectures. Here is a YouTube Playlist of the lectures.

University of Warwick

Welcome Week 2019 (Week 0): Lecturer for MA9010 Fundamental Tools (Linear Algebra and Differential Equations).

Spring Term 2019 (Term 2): Lecturer for MA252 Combinatorial Optimisation. See the topics covered and schedule of the lectures.

Welcome Week 2018 (Week 0): Lecturer for MA9010 Fundamental Tools (Linear Algebra and Differential Equations).

ETH Zürich

Spring Semester 2017: Course Organizer for Analysis II for Mechanical Engineering and Material Science.

Autumn Semester 2016: Course Organizer for Analysis I for Mechanical Engineering and Material Science.

University of Oxford

Michaelmas Term 2015: Class Tutor for C8.3 Combinatorics.

Hilary Term 2015: Class Tutor for B8.5 Graph Theory.

Michaelmas Term 2014: Class Tutor for C8.3 Combinatorics.

Hilary Term 2014: Teaching Assistant for B8.5 Graph Theory.

Michaelmas Term 2013: Teaching Assistant for C8.3 Combinatorics.

Thompson Rivers University

2009-2011: Worked at the Mathematics Help Centre.

Online Combinatorics Talks and Lectures

Research Level:

• Will Perkins: On statistical mechanics methods in combinatorics at the CombGeo Lab at the Moscow Institute of Physics and Technology.

• Woijciech Samotij: The Container Method at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Peter Keevash: The Existence of Designs at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Ehud Friedgut: Analysis of Boolean Functions on Graph Products, Dictatorships and Juntas at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Irit Dinur: Direct Products of Games and Graphs at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• David Steurer: Sum of Squares Method at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Alexandru Nica: Combinatorial Aspects of Free Probability Theory at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Alexander Postnikov: Combinatorics of the Grassmanian at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Joel Hass: Knots at the 18th Midrasha Mathematicae at the Israel Institute for Advanced Study.

• Vitaly Bergelson: Mutually enriching connections between ergodic theory and combinatorics at CIRM.

• Andrew Marks: Descriptive graph combinatorics at CIRM.

• Jennifer Chayes and Christian Borgs: Graphons and graphexes as limits of sparse graphs at CIRM.

• Shachar Lovett: Information Theory in Combinatorics at the Simons Institute.

• Nati Linial: Some Geometric Perspectives on Combinatorics: High-Dimensional, Local and Local-to-Global at the Simons Institute.

Graduate Student Level:

• Timothy Gowers: Topics in Combinatorics at the University of Cambridge.

• Po-Shen Loh: Extremal Combinatorics at Carnegie Mellon University.

• Yufei Zhao: Graph Theory and Additive Combinatorics at MIT.

• Sang-il Oum: Combinatorics at KAIST.

• Luke Postle: Graph Theory at Waterloo.

• Luke Postle: Probabilistic Methods at Waterloo.

• Steve Butler: Spectral Graph Theory at Iowa State University.

• Ryan O'Donnell: Analysis of Boolean Functions at Carnegie Mellon University.

• Remco van der Hofstad: Complex Graphs and Networks at IMPA.

• Jonathan Noel: Extremal Combinatorics at the University of Victoria.

Introductory Level:

• Sang-il Oum: Introduction to Graph Theory at KAIST.

• Matt DeVos: Introduction to Graph Theory at SFU.

• Erik Demaine, Srini Devadas and Victor Costan: Introduction to Algorithms at MIT.

• Tom Trotter: Applied Combinatorics at Georgia Institute of Technology.

• Sami Assaf: Various Courses at USC.

• Trefor Bazett: Discrete Math at the University of Victoria.

• Jonathan Noel: Discrete and Combinatorial Mathematics at the University of Victoria.

• Jonathan Noel: Combinatorial Optimisation at the University of Warwick.

Open Problems

Contact

Office: David Turpin Building A435

E-mail: noelj@uvic.ca

Phone: (250) 472-5111