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TZID:Europe/Paris
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UID:8499@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250121T143000
DTEND;TZID=Europe/Paris:20250121T153000
DTSTAMP:20250114T124030Z
URL:https://www.i2m.univ-amu.fr/evenements/tba-182/
SUMMARY:Thomas HUGHES (Université de Bath): Interface evolution in bistabl
 e spatial models: a global approach
DESCRIPTION:Thomas HUGHES: We consider spatial stochastic population models
  exhibiting bistability. In such models\, narrow interfaces tend to form b
 etween regions dominated by one of the two stable states. To understand ho
 w the population evolves\, we may study the dynamics of these interfaces i
 n time. For several bistable population models\, including some variants o
 f the voter model\, it is known from recent work that the limiting interfa
 ces\, under certain rescalings\, follow a geometric evolution called mean 
 curvature flow. Surfaces evolving by mean curvature flow develop singulari
 ties in finite time\, which imposes a short-time constraint and regularity
  assumptions on the convergence results.\n\nIn this talk\, I will first di
 scuss some models exhibiting this phenomenon\, and results concerning thei
 r interfaces. I will then discuss a recent work which uses tools from anal
 ysis\, in particular level-set methods and the theory of viscosity solutio
 ns\, to improve upon recent interface convergence results for a broad clas
 s of bistable stochastic population models. In particular\, we give checka
 ble conditions on an ancestral dual process which guarantee that the inter
 faces converge globally in time to a generalized mean curvature flow.\n\nT
 his is joint work with Jessica Lin (McGill).
CATEGORIES:Séminaire,ALEA,Probabilités
LOCATION:I2M Saint-Charles - Salle de séminaire\, Université Aix-Marseill
 e\, Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, Franc
 e
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Université Aix-Marseille\,
  Campus Saint-Charles\, 3 Place Victor Hugo\, Marseille\, 13003\, France;X
 -APPLE-RADIUS=100;X-TITLE=I2M Saint-Charles - Salle de séminaire:geo:0,0
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TZID:Europe/Paris
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DTSTART:20241027T020000
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