[cmath] CSMQ (22/01/2021) Robert Haslhofer

[Activités CRM]

*******************************************************************
COLLOQUE DES SCIENCES MATHÉMATIQUES DU QUÉBEC
Lauréat du prix de mathématiques André-Aisenstadt 2020 /
2020 André Aisenstadt Prize in Mathematics Recipient

*******************************************************************
DATE :
Le vendredi 22 janvier 2021 / Friday, January 22, 2021

HEURE / TIME :
15 h - 16 h / 3:00 p.m. - 4:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Robert Haslhofer (University of Toronto)
TITRE / TITLE :
Mean curvature flow through neck-singularities

LIEU / PLACE :
Si ce n’est déjà fait, pour recevoir le lien Zoom pour la série, veuillez vous inscrire à: http://crm.umontreal.ca/colloque-sciences-mathematiques-quebec/#csmq
If you have not already done so, to receive the Zoom link for the series, please sign up at: http://crm.umontreal.ca/quebec-mathematical-sciences-colloquium/index.html#csmq


RESUME / ABSTRACT :
A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector.  Mean curvature flow first arose as a model of evolving interfaces and has been extensively studied over the last 40 years.  In this talk, I will give an introduction and overview for a general mathematical audience.  To gain some intuition we will first consider the one-dimensional case of evolving curves.  We will then discuss Huisken’s classical result that the flow of convex surfaces always converges to a round point.  On the other hand, if the initial surface is not convex we will see that the flow typically encounters singularities.  Getting a hold of these singularities is crucial for most striking applications in geometry, topology and physics.  Specifically, singularities can be either of neck-type or conical-type.  We will discuss examples from the 90s, which show, both experimentally and theoretically, that flow through conical singularities is utterly non-unique.  In the last part of the talk, I will report on recent work with Kyeongsu Choi, Or Hershkovits and Brian White, where we proved that mean curvature flow through neck-singularities is unique.  The key for this is a classification result for ancient asymptotically cylindrical flows that describes all possible blowup limits near a neck-singularity.  In particular, this confirms the mean-convex neighborhood conjecture.  Assuming Ilmanen’s multiplicity-one conjecture, we conclude that for embedded two-spheres mean curvature flow through singularities is well-posed.


******************************************************************
Responsable(s) :
Jean-Philippe Lessard (lessard at CRM.UMontreal.CA)
******************************************************************

http://crm.umontreal.ca/colloque-sciences-mathematiques-quebec/#csmq

-------------- next part --------------
An HTML attachment was scrubbed...
URL: https://mail.cms.math.ca/pipermail/cmath/attachments/20210118/6c6abccf/attachment.htm