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H 1 Interview at CIRM: Genevieve Walsh

Auteurs : Walsh, Genevieve (Personne interviewée)
CIRM (Editeur )

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What made you choose math? When did you decide that it would become your profession? Let's talk about your first mathematical memories. When you were still a child. What was your first encounter with mathematics? Let's talk about your research, which areas of mathematics do you focus on? You were the holder of the Jean-Morlet Chair at Cirm and you just finished your chair semester. What were your main reasons for applying? What is the scientific content of your semester, which is jointly organized locally with Luiza Paoluzzi? What are the benefits of this semester for Aix-Marseille, the students here, other researchers and for yourself? Can you tell us about your plans after the Chair? Some publication or book perhaps? You're right in the centre of this special scientific concept focusing on one semester, in charge of a chair on one site. What's your feedback on this? How do you feel about being here at CIRM? What do you think about the place?

Résumé : 'I am a geometric topologist, and I'm interested in problems in both geometric topology and geometric group theory. I study groups acting on spaces in a variety of contexts: groups acting on hyperbolic space with quotient the complement of a knot in S3, groups acting on trees, how to make a "good" space for a group to act on, and the many ways a particular group can act on a particular space. I also like to understand the geometry of these spaces.

I was trained (if a mathematician can be trained) as a 3-manifold topologist. Work that came out of my thesis showed that hyperbolic 2-bridge knot complements are virtually fibered. The relevant point is that every 2-bridge knot complement has a finite cover which is very nice geometrically: it is the complement of a link of great circles in S3. I've studied when a 3-manifold has a cover which contains an embedded incompressible surface, by using eigenspaces of covering group action. That every closed hyperbolic 3-manifold has such a cover is known as the virtually Haken conjecture. My current research on knot complements studies the question of commensurability: When do two manifolds or orbifolds have a common finite-sheeted cover? Commensurability is an equivalence relation on manifolds and orbifolds which is very rich even when restricted to knot complements. It tells us a lot about the geometry of the knot complement. For example, the shape of the cusp of a knot complement restricts its commensurability class.

Recently, I've been working on some questions about groups generated by involutions and the type of spaces they can act on. When does a right-angled Coxeter group act by reflections in hyperbolic space? When does the automorphism group of a reflection group act on a CAT(0) space? My approach to these group theoretical questions is deeply influenced by 3-dimensional hyperbolic manifolds and orbifolds. In turn, geometric group theory informs my research on manifolds and orbifolds.'

CIRM - Chaire Jean-Morlet 2018 - Aix-Marseille Université

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    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume ; Vareilles, Stéphanie
    Langue : Anglais
    Date de publication : 09/08/2018
    Date de captation : 05/07/2018
    Collection : Outreach ; Mathematics Education and Popularization of Mathematics
    Sous collection : Les interviews du CIRM
    Format : MP4 (.mp4) - HD
    Durée : 00:16:11
    Domaine : Mathematics Education & Popularization of Mathematics
    Audience : Grand Public
    Download :

Informations sur la rencontre

Nom de la rencontre : Jean-Morlet Chair: Semester on 'Geometry, Topology, and Group Theory in Low Dimensions'
Organisateurs de la rencontre : Walsh, Genevieve ; Paoluzzi, Luisa
Dates : 01/02/2018 - 31/07/2018
Année de la rencontre : 2018
URL Congrès : https://walsh-paoluzzi.weebly.com/

Citation Data

DOI : 10.24350/CIRM.V.19467703
Cite this video as: Walsh, Genevieve (2018). Interview at CIRM: Genevieve Walsh. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19467703
URI : http://dx.doi.org/10.24350/CIRM.V.19467703