Mean curvature flow and its singularity

Department's Seminar
26 April 2023
Start time 
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1" (Povo 0)
Maths Department
Target audience: 
University community
UniTrento students
Registration email: 
Contact person: 
Proff. V. Agostiniani, A. Oneto, A. Pinamonti, E. Postinghel, M. Stanojkovski
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980-1511
Reto Buzano (University of di Turin)

Abstract:  We will start this talk, which will be told mainly via pictures, with a short introduction to the mean curvature flow and the type of problems one would like to resolve with it. We will see that a major obstacle when trying to apply the flow is its singularity formation. We then discuss two results. First, we show that under some curvature assumptions the singularity formation is sufficiently simple to find ways to flow through the singularities without losing any topological information. (Here, we present joint work with Robert Haslhofer and Or Hershkovits and with Sylvain Mailot.) Second, we show that without such simplifying curvature assumptions the singularities can be arbitrarily complicated by constructing singularity models of any given genus. (This is joint work with Huy Nguyen and Mario Schulz.)

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