On June 9th 2025, we will be holding a one day workshop at Queen Mary University of London. Lectures will take place in the School of Mathematical Sciences, MB505.
Curvature Flows Workshop
School of Mathematical Sciences MB 505 Seminar Room
11am-Noon First Talk - Mat Langford (Australian National University)
Title: Deforming curves-with-boundary by curvature
Abstract: We present a number of recent developments on the deformation of curves-with-boundary by their curvature vector. We consider (compact and non-compact) curves having either two or one boundary points, at which either the Dirichlet or Neumann (a.k.a. free boundary) condition is satisfied. We establish the convergence of solutions (to chords, half-chords, round half-points and, in one exceptional case, half Grim Reapers) and a classification of convex ancient solutions. In both cases, comprehensive results are obtained under Neumann-Neumann (or Dirichlet-Dirichlet) boundary conditions, but some open problems remain in the Dirichlet-Neumann setting. (The project involves collaborations with Jonathan Zhu, Theodora Bourni, Nathan Burns, Spencer Catron, Yuxing Liu, George McNamara and Lekh Bhatia.)
Noon - 2pm Lunch
2pm-3pm Second talk - Mariel Saez (Pontificia Universidad Católica de Chile)
Title: On the existence and classification of k-Yamabe gradient solitons
Abstract: The k-Yamabe problem is a fully non-linear extension of the classical Yamabe problem that seeks for metrics of constant k-curvature. In this talk I will discuss this equation from the point of view of geometric flows and provide existence and classification results for soliton solutions of the k-Yamabe flow in the positive cone.
This is joint work with Maria Fernanda Espinal
3pm-4pm Coffee Break
3:30 - 4:30 pm Third Talk - Alex Mramor (University of Copenhagen)
Title: On the long-term behavior of the mean curvature flow in 3-manifolds
Abstract: In this talk, I discussed recent joint work with Ao Sun where we consider the fate of
the mean curvature flow in closed 3-manifolds. Employing many important recent
advances on the mean curvature flow we can show that almost regular flows, as
introduced by Bamler and Kleiner, will either go extinct in finite time or converge,
possibly with multiplicity, to a minimal surface; by a perturbation argument one
can go on to construct piecewise almost regular flows where the limit, if nonempty,
must be stable. Using this we can use the flow to construct minimal surfaces in
3-manifolds in a variety of circumstances, mainly novel from the point of view that
the arguments are via parabolic methods.
Register for this workshop here