Alice Lacaze-Masmonteil

PIMS-CNRS Postdoctoral Fellow

About me

I am a PIMS-CNRS postdoctoral fellow at the University of Regina working under the supervision of Karen Meagher. In October 2024, I completed my PhD at the University of Ottawa under the supervision of Mateja Šajna. The focus of my doctoral thesis was on cycle decompositions of directed graphs. My thesis received the University of Ottawa Department of Mathematics and Statistics Ph.D. Thesis Award which was awarded to the best PhD thesis in mathematics and statistics completed in 2024. During my PhD, I also visited Daniel Horsley to collaborate at Monash University in Melbourne Australia for a period of seven months.

As a postdoctoral fellow, I want to take the opportunity to establish new collaborations and work on new problems. Although I am not currently looking to start a new project, if you would like to discuss research, please feel free to contact me. Below, I describe a few of my research interests.

  1. Cycle decomposition of graphs: Cycle decomposition problems generally consider the question of existence of a decomposition of a graph into a set of cycles of prescribed lengths. Recently, many fundamental cycle decomposition problems have been solved for graphs. However, the directed analogue of each of these problems remains open. My doctoral thesis focussed on two fundamental problems related to cycle decompositions of directed graphs. Presently, I am working on generalizing the methods developed in my thesis to a much more general case of the directed Oberwolfach problem.
  2. Pursuit-evasion games on graphs: Given an intruder on a graph, a set of cops is tasked with capturing this intruder in as few turns as possible. A fundamental problem is to determine the minimum number of cops required to capture this intruder within a finite number of turn on a given graph. This parameter is known as the copnumber. I am presently interested in variations of this game in which the intruder is given the power to eliminate a cop under certain circumstances.
  3. The perfect matching association scheme: The perfect matching association scheme is a set of graphs whose vertices are the perfect matchings of the complete graph and for which adjacencies are dictated by the cycle structure of the union of any two perfect matchings. Currently, I am interested in maximum cliques in graphs that arise from the union of certain graphs in this scheme. I am also interested in questions related to the diameter and chromatic number of graphs in the perfect matching association scheme.