2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
An invitation to low-dimensional topology
Org: Adam Clay (University of Manitoba) and Patrick Naylor (McMaster University)
[PDF]
Org: Adam Clay (University of Manitoba) and Patrick Naylor (McMaster University)
[PDF]
- HANS BODEN, McMaster
- MAXIME FORTIER BOURQUE, UdeM
- STEVE BOYER, UQAM
- TYRONE GHASWALA, University of Waterloo
Does the Loch Ness Monster's mapping class group even have a finite-index subgroup? [PDF]
- MAXIME FORTIER BOURQUE, UdeM
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The study of mapping class groups of infinite-type surfaces (so called big mapping class groups) has enjoyed a surge of interest in the past decade or so. Remarkably, the seemingly innocent question in the title of this talk remains stubbornly unresolved.
I will motivate the question, introducing the relevant results from the study of infinite-type surfaces, with the aim of convincing you it's a compelling question! I will not assume familiarity with big mapping class groups.
I have thought about the question on and off for the past few years, and I invite, with open arms, any ideas anyone may have!
- OFFICE HOURS
- OFFICE HOURS
- DUNCAN MCCOY, UQAM
- KASRA RAFI, University of Toronto
From Mirzakhani’s Volumes to Random Surfaces [PDF]
- OFFICE HOURS
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We will explore what it means to choose a random geometric surface, using natural probability measures on moduli space, and describe some of the limiting geometric phenomena that emerge for high genus surfaces. In this setting, many geometric features stabilize as the genus tends to infinity and, somewhat paradoxically, become easier to describe and compute, for example the distribution of short geodesics and the geometry of a typical neighborhood of a random point. This perspective was initiated by Mirzakhani, who used Weil-Petersson volume to define a natural notion of a random hyperbolic surface and to calculate expected values of various geometric quantities. I will explain these ideas and then discuss analogous questions and results for flat surfaces, highlighting connections between geometry, dynamics and low-dimensional topology.
- YVON VERBERNE, The University of Western Ontario
Grand arcs and the Nielsen-Thurston Classification [PDF]
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The Nielsen-Thurston classification tells us that the elements in the mapping class group of a finite type surface are either finite order, reducible, or pseudo-Anosov. We discuss this classification and how to obtain a similar classification theorem when one considers the action of the mapping class group on a combinatorial complex. In the case of infinite type surfaces, the question of what a classification type theorem for elements in the mapping class group would be is open. In this talk, we will discuss what a generalization of a pseudo-Anosov mapping class may be in the context of the action of the mapping class group on a combinatorial complex, and open problems which surround this approach.
- C.M. MICHAEL WONG, University of Ottawa