Applications are closed
for this workshop

Geometric flows and Riemannian geometry

September 21 to September 25, 2015

at the

American Institute of Mathematics, San Jose, California

organized by

Lei Ni and Burkhard Wilking

This workshop, sponsored by AIM and the NSF, will be devoted to geometric flows and Riemannian geometry.

The main topics of the workshop are:

  • The Ricci flow and manifolds with positive curvature

    The Ricci flow is effective in proving results on the diffeomorphic topological type of manifolds satisfying various positivity assumptions. But there are still many problems that remain open. Interactions between various methods can advance the understandings. A notorious difficult problem in Alexandrov geometry is to smooth singular spaces with lower curvature bound. In particular situations though, one can hope to define a Ricci flow with singular initial data.

  • Hypersurface flow, minimal surfaces and eigenvalue estimates

    Some effective estimates have been developed for various geometric flow by a `de-regularization' procedure. Typical example is to use the continuity modulus to replace the gradient estimate, expansion modulus to replace the Hessian estimates, Andrews noncollapsing quantity to replace the length of the second fundamental form. These can be used to prove various conjectures involving the eigenvalue estimates and uniquness/rigidity result regarding surfaces with prescribed conditions on the principle curvatures. But there are still problems open.

  • Convex geometry and Gauss curvature flow

    Fully nonlinear flows on convex surfaces involves both PDE techniques and understandings of convex geometry, which in turn is related to the study of manifolds with positive curvature.

The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.

The deadline to apply for support to participate in this workshop has passed.

For more information email workshops@aimath.org


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