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DTSTART:20240310T070000
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DTSTART:20231105T060000
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UID:69f930780c448
DTSTART;TZID=America/Toronto:20240923T143000
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DTEND;TZID=America/Toronto:20240923T153000
URL:https://uwaterloo.ca/pure-mathematics/events/pure-math-dept-colloquium
SUMMARY:Pure Math Dept Colloquium
CLASS:PUBLIC
DESCRIPTION:ROBERT HASLHOFER\, UNIVERSITY OF TORONTO\n\nMean curvature flow
  through singularities\n\nA family of surfaces moves by mean curvature flo
 w if the velocity at\neach point is given by the mean curvature vector. Me
 an curvature flow\nfirst arose as a model of evolving interfaces in materi
 al science and\nhas been extensively studied over the last 40 years. In th
 is talk\, I\nwill give an introduction and overview for a general mathemat
 ical\naudience. To gain some intuition we will first consider the\none-dim
 ensional case of evolving curves. We will then discuss\nHuisken's classica
 l result that the flow of convex surfaces always\nconverges to a round poi
 nt. On the other hand\, if the initial surface\nis not convex we will see 
 that the flow typically encounters\nsingularities. Getting a hold of these
  singularities is crucial for\nmost striking applications in geometry\, to
 pology and physics. In\nparticular\, we will see that flow through conical
  singularities is\nnonunique\, but flow through neck singularities is uniq
 ue. Finally\, I\nwill report on recent work with various collaborators on 
 the\nclassification of noncollapsed singularities in R^4.\n\nMC 5501
DTSTAMP:20260504T234912Z
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