I am always looking for Undergraduate, Master's and PhD students and Postdoctoral Researchers to work with. 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
Students and Postdocs
Current students and postdocs:
• Joseph Hyde
. University of Victoria. Started in August 2022. Co-supervised with Natasha Morrison
and Bruce Reed
• Natalie Behegue
. University of Victoria. Started in January 2022. Co-supervised with Natasha Morrison
• Jae-baek Lee. University of Victoria. Started in January 2021. Co-supervised with Gary MacGillivray
• Ashna Wright. University of Victoria. Started in September 2022. Co-supervised with Natasha Morrison
Undergraduate Honours Students:
• Gabriel Crudele. University of Victoria. Started in September 2022. Co-supervised with Peter Dukes Soon to be a Master's Student at McGill University
My current students can find more information by navigating to this page
• Please check out the application requirements
• Abel Romer
. University of Victoria. Tight Bounds on 3-Neighbor Bootstrap Percolation
. 2020-2022. Co-supervised with Peter Dukes
• Vincent Pfenninger
. Graph Bootstrap Processes in Complete Bipartite Graphs.
ETH Zürich, Spring Semester 2017. Co-supervised with Benny Sudakov
. Now a Research Fellow at the University of Birmingham
Undergraduate Research Students:
• Elena Moss
. University of Victoria. NSERC USRA Summer Research Student. May-Aug 2022.
• Gabriel Crudele. University of Victoria. Summer Research Student. May-Aug 2022. Co-supervised with Peter Dukes
. Soon to be a Master's Student at McGill University
• Lina Maria Simbaqueba Marin. University of Victoria. Mitacs Globalink Research Intern from Universidad Nacional de Colombia. May-Aug 2022.
• Arjun Ranganathan. On the Running Time of Hypergraph Bootstrap Percolation
. Research Intern from IISER, Pune. June 2021-May 2022.
• Joe Wall
. Saturation and Weak Saturation.
University of Warwick, URSS Program, Summer 2018. Now a PhD student at Lancaster University
• Adam Finchett
. Graph Limits, Norms and Applications.
4th Year Essay. University of Warwick, 2019/2020. Now a Data Engineer at Kubrick Group
• Matt Pike. Problems in Bootstrap Percolation.
4th Year Essay. University of Warwick, 2018/2019.
• Rachel Hardgrave. Classical Theorems in List Colouring.
3rd Year Essay. University of Warwick, 2019/2020.
• Sophia Werner. Semi-Definite Programming.
3rd Year Essay. University of Warwick, 2018/2019.
• Stefan Lochau
. Entropy and Linear Programming Methods for Counting Matchings and Independent Sets in Graphs.
Bachelor Thesis. ETH Zürich, Autumn Semester 2016. Now a software engineer at M&F Engineering AG
. Co-supervised with Benny Sudakov
Philosophy and Advice
I hope to write some of my own advice to students in the future but, for now, let me share some great advice from those who are much more wise and experienced than I am.
— 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 Guidlines 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
— Serre's advice on How to Write Mathematics Badly
— 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?
Equity, Diversity and Inclusion:
Members of underrepresented groups face special obstacles in the mathematical sciences, and in academia more broadly. Academia as a whole is still in the process of understanding and recognizing these challenges and learning how to overcome them. The advice above, while valuable to early career researchers of all backgrounds, rarely acknowledges these additional hurdles. Most of these articles were written when our understanding was far less developed than it is now.
I believe that it is crucial for all members of my research group to be comfortable and confident to interact with one another. To this end, I encourage my students, postdocs and colleagues to think about issues of equity, diversity and inclusion and to employ inclusive practices. For more information, I suggest looking at the following:
— UVic's Policy on Human Rights, Equity and Fairness
— The webpage for the Math & Statistics Equity, Diversity and Inclusion (MSEDI) committee
— the Association for Women in Mathematics UVic Student Chapter
— 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. They also have an excellent weekly colloquium.
There's lots of different ways for students and postdocs to fund their research at UVic and elsewhere. Below, I list a few opportunities that I'm aware of. This is by no means a comprehensive list and I suggest searching the UVic webpage or other sources for more information.
• NSERC Undergraduate Student Research Awards
• UVic Science Undergraduate Research Awards (SURA)
• UVic Jamie Cassels Undergraduate Research Awards (JCURA)
• More information about USRA, SURA and JCURA in the UVic Math & Stats Department can be found here
• UVic Boehm Family Award for Undergraduate Travel
International Undergraduate Research Internships
• Mitacs Globalink Research Internship
• 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
• 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.
• 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.
• 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
• Mitacs Globalink Early Career Fellowship – China
are for Chinese postdoctoral fellows to work in Canada
• 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 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
• 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.
• 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
As an early career researcher, it is important to start familiarizing yourself with the open problems in the area. This includes the central problems, which tend to be "old" and have many papers written about them, as well as the interesting questions arising from more recent work. Problems of the latter type tend to be more approachable for students and, at the same time, harder for students to come across.
I strongly recommend
new researchers in combinatorics to subscribe to e-mail updates for new articles posted to math.CO on arxiv
. This will keep you updated on the latest results and open problems in the area.
Current or prospective students of mine should feel free to e-mail me
about the types of problems that I am interested in working on. I will happily provide a copy of my NSERC Discovery Grant application which describes the general direction of my research program as well as many specific open problems.
Another way to become integrated into the research community and stay up to date on the latest developments is by attending conferences and workshops. This is a great way to make valuable connections and learn about open problems (new and old). Doug West maintains a webpage
which serves as a rather comprehensive list of events in combinatorics.
Below, I have compiled a list of links to open problems. Disclaimer:
I do not guarantee that these problems are still open!
• Barbados Graph Theory Workshop: 2022
• BIRS Workshop on "New Perspectives in Colouring and Structure": 2020
• Matroid Union open problem session (2020)
• Structural Graph Theory Workshop at Gułtowy: 2019
• Workshop on Combinatorial Reconfiguration: 2019
• Fortaleza Workshop on Combinatorics: 2019
• Workshop Cycles and Colourings: 2018
• Mittag-Leffler programme on Graphs, Hypergraphs, and Computing: 2014
• Graduate Research Workshop in Combinatorics: multiple years
• Graphs and Randomness at IMPA: 2018
• Midrasha Mathematicae: In and Around Combinatorics: 2015
• Beyond Randomized Rounding and the Probabilistic Method at the Simons Institute: 2019
• The Egeváry Research Group maintains an open problem forum called Egres Open
• Alexey Pokrovskiy's open problem page
• Louis Esperet's open problem page
• Stefan Steinerberger's open problem list
• Joshua Cooper's open problem page
• Boris Bukh's open problem page
• Doug West's open problem page
• Jerry Spinrad's open problem page
• The Rutgers DIMACS page on open problems for undergraduates
• Open problems
from Bondy and Murty's book.
• Open problems from Schrijver's book "Combinatorial Optimization - Polyhedra and Efficiency" can be found here
• Some of Erdős' (many) problem papers: Fan Chung's list
, another list maintained by Fan Chung
• Also check out the Open Problem Garden