Karen Gunderson

Department of Mathematics
University of Manitoba
336 University Centre
Email: karen.gunderson@umanitoba.ca

Research

Random graphs, extremal combinatorics, percolation.

Combinatorics Seminar

Co-organizer of the University of Manitoba Combinatorics Seminar.
Held weekly during term-time: Thursdays at 11:30 am.
Previous seminar listings, can be found here.

Research students

Students who are interested in pursuing graduate studies (M.Sc., Ph.D.) under my supervision should contact me by email.

Undergraduate students interested in working with me on a summer research project are welcome to contact me. For students from the University of Manitoba, some of the following funding opportunities are available:

NSERC and Faculty of Science Undergraduate Student Research Awards (Deadline is likely in December or January)
University of Manitoba Undergraduate Research Awards (Deadline is likely in January or February).

Undergraduate students from abroad who are interested in working with me may be able to apply for a Mitacs Globalink Research Internship. The application process begins in late summer or early fall. While all applications are submitted through Mitacs, I would be happy to discuss the details with any interested students.

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Publications

Published and appearing

Burning the plane: densities of the infinite Cartesian grid, Graphs Combin. 36 (2020), 1311-1335. (with Anthony Bonato and Amy Shaw) arXiv:1806.05642 [math.CO]
Minimum degree conditions for small percolating sets in bootstrap percolation, Electronic J. Combinatorics 27 (2020), P2.37, arXiv:1703.10741 [math.CO].
Random Geometric Graphs and Isometries of Normed Spaces, Trans. Amer. Math. Soc. 370 (2018), 7361-7389. (with Paul Balister, Béla Bollobás, Imre Leader, and Mark Walters) arXiv:1504.05324 [math.FA]
Tournaments, 4-uniform hypergraphs, and an exact extremal result, J. Combin. Theory Ser. B 126 (2017), 114-136. (with Jason Semeraro) arXiv:1509.03268 [math.CO]
The time of graph bootstrap percolation, Rand. Structures Algorithms 51 (2017), 143-168. (with Sebastian Koch and Michał Przykucki) arXiv:1503.01454 [math.PR]
Almost Separable Matrices, J. Comb. Optim. 33 (2017), 215-236. (with Matthew Aldridge and Leonardo Baldassini) arXiv:1410.1826 [math.CO] journal
Positive independence densities of finite rank countable hypergraphs are achieved by finite hypergraphs, European J. Combin. 57 (2016), 85-93. (with Paul Balister and Béla Bollobás) arXiv:1505.08044 [math.CO]
Random Markov processes for countable and uncountable alphabets, Israel J. Math. 216 (2016), 181-214. (with Neal Bushaw and Steven Kalikow) arXiv:1410.1457 [math.PR]
Bounding the number of hyperedges in friendship r-hypergraphs, European J. of Comb. 51 (2016), 125-134. (with Natasha Morrison and Jason Semeraro) arXiv:1412.5822 [math.CO], journal
A sharp threshold for a modified bootstrap percolation with recovery, Journal of Statistical Physics 157 (2014), 531-570. (with Tom Coker) arXiv:1505.08030 [math.PR], journal
Lower bounds for bootstrap percolation on Galton-Watson trees, Electron. Commun. Probab. 19 (2014), article 42, 7 pages. available at arXiv:1402.4462 (with Michał Przykucki) arXiv:1402.4462 [math.PR], journal
Bootstrap percolation on Galton-Watson trees, Electron. J. Probab. 19 (2014), paper 13, 1-27. (with Béla Bollobás, Cecilia Holmgren, Svante Janson and Michał Przykucki) arXiv:1304.2260 [math.PR], journal
The adjacent vertex distinguishing total chromatic number, Discrete Math. 312 (2012), 2741-2750. (with Tom Coker) arXiv:1009.1785v2 [math.CO], journal
On combinatorial upper bounds for van der Waerden numbers W(3;r), Proceedings of the Thirty-Ninth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 190 (2008), 33-46. (with David S. Gunderson)

Submitted

Robustness of Erdos-Ko-Rado theorems on permutations and perfect matchings, 36 pages. (with Karen Meagher, Joy Morris, Venkata Raghu Tej Pantangi, and Mahsa N. Shirazi) arXiv:2406.15739 [math.CO]
Induced forests in some distance-regular graphs, 14 pages. (with Karen Meagher, Joy Morris, and Venkata Raghu Tej Pantangi) arXiv:2301.05207 [math.CO]
Adversarial graph burning densities, 13 pages. (with William Kellough, JD Nir, and Hritik Punj) arXiv:2211.15622 [math.CO]
The oriented chromatic number of random graphs of bounded degree, 49 pages (with JD Nir) arXiv:2202.12323
Turán numbers and switching, 17 pages (with Jason Semeraro) arXiv:2204.10775
Limited packings of closed neighbourhoods in graphs, 10 pages. (with Paul Balister and Béla Bollobás) arXiv:1501.01833 [math.CO]

Workshops and Conferences organized

MMMM Graduate Combinatorics Student Workshop, University of Manitoba, 29 April - 1 May 2016.
2016 Prairie Discrete Math Workshop, University of Manitoba, 16-17 May 2016.
2023 CanaDAM (co-chair of local arrangements committee), University of Manitoba and University of Winnipeg, 5-8 June 2023.
2023 Movement & Symmetry in Graphs Research Retreat, University of Manitoba, 9-10 June 2023.