Postal address:Département de mathématiques,Université du Québec à Montréal,PO Box 8888, centre-ville,Montréal H3C 3P8,Québec, Canada
Canada Research Chair in Low Dimensional Topology
Since June 2023, the Canada Research Chair has been providing invaluable support to the low dimensional topology research group at UQAM as well as helping to sustain related activities across the wider Montreal area.
Context
Low-dimensional topology is the subfield of mathematics that studies the shape and geometry of objects in four or fewer dimensions. Whilst manifolds of all dimensions are fundamental to mathematics and appear naturally in physics and other disciplines, the understanding of manifolds of three and four dimensions are a source of important problems in modern mathematics. Firstly, since our daily experience is of a low-dimensional world, it is natural to consider examples and phenomena in these dimensions. Secondly, and more abstractly, understanding dimensions three and four present difficulties that do not arise in higher dimensions. For example, the simplest five dimensional manifolds were classified in the 1960s, however the corresponding classification was only achieved for three dimensional manifolds in the 2000s with the resolution of the Poincaré conjecture and the classification in four dimensions remains open to this day.
Researchers
The Chair has been supporting the following doctoral and post-doctoral researchers:
Robert Harris:
Robert is currently a post-doc at UQAM having started here in September 2025. He received his PhD from the University of Waterloo in 2025 under the supervision of Doug Park. Robert specializes in the topology of smooth 4-dimensional manifolds with a particular interest in the construction of exotic smooth structures on definite 4-manifolds with small fundamental groups.Connor Sell :
Connor is currently a post-doc at UQAM having started here in September 2023. He received his PhD from Rice University in 2023 under the supervision of Alan Reid. Connor's area of expertise is the topology of hyperbolic manifolds and arithmetic manifolds more generally.Bojun Zhao :
Bojun is currently a post-doc at UQAM having started here in September 2024. He is currently in Berkeley for the SLMath program on Topological and Geometric Structures in Low Dimensions. He received his PhD from Buffalo University in 2024 under the supervision of Xingru Zhang. Bojun is interested in the topics related to left orderable 3-manifold groups, taut foliations and pseudo-Anosov flows of 3-manifolds.Chi Cheuk Tsang :
Chi Cheuk was a post-doc at UQAM from September 2023 to December 2025. He is currently in Berkeley for the SLMath program on Topological and Geometric Structures in Low Dimensions. In Autumn 2026, Chi Cheuk will be taking up a tenure track position at Tongji University. He received his PhD from UC Berkeley in 2023 under the supervision of Ian Agol.Iuliia Popova:
Iuliia is a PhD student at UQAM who started in September 2023. Her doctoral research involves applying methods from Heegaard Floer homology to conjectures relating to Dehn surgery and Seifert fibered spaces. Iuliia completed her masters' at Université de Génève where she carried out research on extended link signatures.Giacomo Bascape:
Giacomo completed his PhD at UQAM in August 2025. Motivated by questions about instanton Floer homology, Giacomo developed methods to understand which 3-manifolds have SU(2)-abelian fundamental groups. Since his PhD he has taken up a job at IBM.Patricia Sorya:
Patricia completed her PhD at UQAM in August 2025. In her thesis she developed results about characterizing slopes of knots in the 3-sphere with the most striking results obtained in the case of satellite knots. Her thesis was awarded the 2025 Carl Herz prize by the ISM. She currently holds an NSERC post-doc based at the University of Ottawa.
Events
Funds from the Chair were used to support mathematical events. Four workshops in the 2025 CRM thematic semester Topological and geometric structures in low dimensions were partially supported by funds from the Chair.
Topological 4-manifolds (July 2 - 11, 2025)
The aim of this workshop was to showcase recent work on topological 4-manifolds and give an overview of what is known and what remains to be done. The associated minicourses were designed to serve as an introduction to the fundamental techniques of the area. The topics for the conference also encompassed aspects of knot theory that concern topological 4-manifolds such as topological slicing and concordance.Knots, groups and manifolds (August 11 - 15, 2025)
This conference was centred around current developments in knot theory, group theory and manifolds of dimensions 3 and 4 inspired by the enduring mathematical legacy of Cameron Gordon. The talks included retrospectives of the impact of some of Gordon's work, as well as research talks by both senior and junior researchers.Low dimensional topology and Floer homology (August 18 - 29, 2025)
The aim of this workshop was to showcase recent developments in Floer theory and related areas as well as their applications in low-dimensional topology. Specific areas of focus included relationships between Floer homology and Dehn surgery, exotic 4-manifolds, and geometric structures on 3-manifolds like taut foliations and pseudo-Anosov flows.Hyperbolic manifolds in dimensions 4 (and more) (September 2 - 12, 2025)
The goal of this workshop was to bring together researchers working in the areas of higher dimensional hyperbolic manifolds and low-dimensional topology and geometry to map out the current state of the field, to underline major problems going forward and to develop new methods for analysing them. The workshop aimed to create a synergy between researchers with different backgrounds but with a common focus on developing tools to study the geometry and topology of hyperbolic manifolds in dimensions 4 and higher.