**E-mail:** noelj@uvic.ca

### ICMS Young Researchers in Combinatorics Workshop

Shagnik Das, Carla Groenland, Yanitsa Pehova and I are organising a workshop for Young Researchers in Combinatorics at the International Centre for Mathematical Sciences in Edinburgh on July 18-22, 2022 (rescheduled due to COVID-19). See the webpage.

### Internship Opportunity

I have submitted proposals to Mitacs for Globalink Research Internships for Summer 2022. International undergraduate students who are interested to come to Canada for a research internship are encouraged to apply. The application period is August-September, 2021.

### Research Papers

**Topics:** Extremal Combinatorics Probabilistic Combinatorics Combinatorial Limits Bootstrap Percolation Graph Colouring Computational Complexity check all uncheck all

** Submitted**

**1.** *Pirates in Wonderland: Liquid Democracy has Bicritical Guarantees* (with Mashbat Suzuki and Adrian Vetta). Submitted.

** Published, to Appear or Accepted**

**2.** *A Sharp Threshold for Bootstrap Percolation in a Random Hypergraph* (with Natasha Morrison). Accepted to Electron. J. Probab. (pr/boot)

**3.** *Non-bipartite k-common graphs* (with Daniel Kráľ, Sergey Norin, Jan Volec and Fan Wei). Accepted to Combinatorica. (ext/lim)

**4.** *Cyclic Coloring of Plane Graphs with Maximum Face Size 16 and 17* (with Zdeněk Dvořák, Michael Hebdige, Filip Hlásek and Daniel Kráľ). European J. Combin. 94 (2021) 103287 (col)

**5.** *Bounding the number of cycles in a graph in terms of its degree sequence* (with Zdeněk Dvořák, Natasha Morrison, Sergey Norin and Luke Postle). European J. Combin. 91 (2021) 103206 (ext)

**6.** *Cycles of length three and four in tournaments* (with Timothy F. N. Chan, Andrzej Grzesik and Daniel Kráľ). J. Combin. Theory Ser. A. 175 (2020) 105276 (ext/lim)

**7.** *Characterization of quasirandom permutations by a pattern sum* (with Timothy F. N. Chan, Daniel Kráľ, Yanitsa Pehova,
Maryam Sharifzadeh and Jan Volec). Random Structures & Algorithms 57(4) (2020) 920--939. (pr/lim)

**8.** *Reconfiguring Graph Homomorphisms on the Sphere* (with Jae-Baek Lee and Mark Siggers). European J. Combin. 86 (2020) 103086. (cc/col)

**9.** *Graph Homomorphism Reconfiguration and Frozen H-Colourings* (with Richard C. Brewster, Jae-Baek Lee, Benjamin Moore and Mark Siggers). J. Graph Theory 94 (3) (2020) 398--420. (cc/col)

**10.** *Finitely forcible graphons with an almost arbitrary structure* (with Daniel Kráľ, László Miklós Lovász and
Jakub Sosnovec). Discrete Anal. Paper 9 (2019) 36 pages. (ext/lim)

**11.** *Extremal Bounds for Bootstrap Percolation in the Hypercube* (with Natasha Morrison). J. Combin. Theory Ser. A 156 (2018) 61--84. (ext/boot)

**12.** *Weak regularity and finitely forcible graph limits* (with Jacob W. Cooper, Tomáš Kaiser and Daniel Kráľ). Trans. Amer. Math. Soc. 370 (6) (2018) 3833--3864. (ext/lim)

**13.** *Supersaturation in Posets and Applications Involving the Container Method* (with Alex Scott and Benny Sudakov). J. Combin. Theory Ser. A 154 (2018) 247--284. (ext/pr)

**14.** *Saturation in the Hypercube and Bootstrap Percolation* (with Natasha Morrison and Alex Scott). Combin. Probab. Comput. 26 (1) (2017) 78--98. (ext/boot)

**15.** *A Dichotomy Theorem for Circular Colouring Reconfiguration* (with Richard C. Brewster, Sean McGuinness and Benjamin Moore). Theoret. Comput. Sci. (639) (2016) 1--13. (cc/col)

**16.** *Mixing Homomorphisms, Recolorings, and Extending Circular Precolorings* (with Richard C. Brewster). J. Graph Theory 80 (3) (2015) 173--198. (col)

**17.** *A Proof of a Conjecture of Ohba* (with Bruce A. Reed and Hehui Wu). J. Graph Theory 79 (2) (2015) 86--102. (col)

**18.** *Beyond Ohba's Conjecture: A bound on the choice number of k-chromatic graphs with n vertices* (with Douglas B. West, Hehui Wu and Xuding Zhu). European J. Combin. 43 (2015) 295--305. (col)

**19.** *On Saturated k-Sperner Systems* (with Natasha Morrison and Alex Scott). Electron. J. Combin. 21 (3) (2014) #P3.22. (ext)

**20.** *Extending precolourings of circular cliques* (with Richard C. Brewster). Discrete Math. 312 (1) (2012) 35--41. (col)

### Education and Theses

**DPhil (PhD) Mathematics **

University of Oxford

Defended: June 17, 2016

DPhil Thesis: Extremal Combinatorics, Graph Limits and Computational Complexity

Adviser: Alex Scott

**M.Sc. Mathematics**

McGill University

April 2013

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

Adviser: Bruce Reed

**B.Sc. (Hons) Mathematics **

Thompson Rivers University

April 2011

Honours Thesis: The Invariant Subspace Problem

Adviser: Robb Fry