Singularities of Mean Curvature Flow and Related Topics

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2019. The deadline for funded applications was 31 January 2019.

Geometric Analysis, and in particular Geometric Flows, led to some of the most important breakthroughs in pure mathematics in the last decades. This modern area of mathematics combines Differential Geometry (algebraic structures of geometric objects and local control of geometric properties such as curvature) with tools from Analysis (mainly partial differential equations and the calculus of variations) to obtain global differential topological results. As the partial differential equations that are involved are generally non-linear, they often give rise to singularities. In many interesting problems, it is important to understand when and how these singularities occur and to study precise characterisations of them.

An illustrative example is the Mean Curvature Flow. This flow evolves an initial manifold towards an object with more symmetries, for example a potato-shaped surface is transformed to a perfectly round sphere. In more general situations however, the flow develops local singularities where the curvature becomes infinitely large while staying bounded in other regions. Another example is the Ricci Flow, which can be seen as the intrinsic sibling of Mean Curvature Flow, used by Perelman to resolve the Poincaré and Geometrization conjectures – for which he won a Clay Millennium Prize and a Fields Medal.

Dr. Reto Buzano (born Reto Müller) and Dr. Huy The Nguyen both study the singularity formation in Mean Curvature Flow as well as other geometric flows such as Ricci Flow, Willmore, or Harmonic Ricci Flow, and related topics in Geometric Analysis. We are looking for PhD students to join our active group to conduct research in mean curvature flow or related areas. We will be offering projects specifically in high codimension mean curvature flow, mean curvature flow in curved background spaces and the singularity formation in weak mean curvature flow.

With a very active research group in Geometric Analysis (currently involving Reto Buzano, Huy Nguyen, Arick Shao, as well as four PhD students and regular visiting students) as well as with a strong relativity group to interact with and other London universities with active research in Analysis and Geometry in close proximity, Queen Mary University of London has become one of the most interesting places to pursue a PhD in Geometric Analysis. The group will be expanding in 2019, with the addition of a further two postdoctoral research associates funded by the EPSRC grant “Advances in Mean Curvature Flow: Theory and Applications”.

We strongly encourage applications of motivated candidates with a strong background in at least one of the two fields of Analysis and Geometry. If interested, please contact Reto Buzano or Huy Nguyen by e-mail for further information and advice on the application procedure.