Summer Term 2012

 

Brian Krummel (University of Cambridge). The regularity and existence of branched minimal submanifolds. Thursday May 3rd, Huxley 658, 1.30-2.30 pm.
Multivalued functions arise naturally in the study of the branch set of branched minimal immersions. Simon and Wickramasekera (2007) showed how to construct a large class of multivalued solutions in C^{1,\mu} to the Dirichlet problem for the minimal surface equation provided the boundary data satisfied a k-fold symmetry condition. I will extend their existence result, which was specific to the minimal surface equation, to show that there exists multivalued solutions in C^{1,\mu} to other elliptic equations and to elliptic systems that preserve the k-fold symmetry condition. I also will show that the branch sets of the minimal hypersurfaces they constructed are real analytic submanifolds, which involves proving a general regularity result for multivalued solutions to elliptic equations.

 

Special event: Warwick-Imperial-Cambridge Geometric Analysis Seminar. Thursday May 10th, in Warwick.

  • Fernando Codá Marques (IMPA)
  • Francesco Maggi (Florence/UT-Austin)
  • Sergiu Klainerman (Princeton)

Details can be found here: http://go.warwick.ac.uk/mathsevents.

 

Diarmuid Crowley (Max Planck Institute, Bonn). On classifying simply connected 7-manifolds. Thursday May 17th, Huxley 140, 1.00-2.00 pm.
Dimension 7 has a rich history and an active present in both differential topology and geometry. In this talk I give an over view of smooth classification results for simply connected 7-manifolds illustrated by examples of geometric interest. A persistent challenge for 7-manifold topology is to find intrinsic calculations of invariants without using a co-bounding 8-manifolds and global analysis often meets this challenge. For example, with Goette we showed recently how to use the \eta-invariants of the Dirac operator twisted by quaternionic line bundles to define interesting new intrinsic invariants for spin 7-manifolds.

 

Jason Lotay (University College London). TBA. Thursday May 24th, Huxley 140, 1.00-2.00 pm.

 

André Neves (Imperial College). Min-Max Theory and the Willmore conjecture. Thursday May 31st, Huxley 140, 1.00-2.00 pm.

 

Nicolaos Kapouleas (Brown University). TBA. Thursday June 7th, Huxley 140, 1.00-2.00 pm.