I have been spending my sabbatical this year at MSRI and the University of California, Berkeley.  I cannot complain about the great interaction with faculty from all over the world, and the wonderful “sunny and 65” days in the Bay area.  So why did I spend last week at the Banff National Park in Canada, surrounded by spectacular mountains with blowing wind and snow?

I was invited to attend a workshop at the Banff International Research Station (BIRS) on geometry.  The main objective of this meeting was to discuss recent ideas and problems in discrete geometry, geometric measure theory and asymptotic geometric analysis.  At first, I feared that my work (mostly focusing on discrete topology and geometric combinatorics) would be too far afield from the rest of the participants.  However, the group (pictured below) were such a diverse (and good looking) collection of individuals, all interested in geometric ideas.

Group Photo 1

Instead of giving an overall description, I thought I would share some of the wonderful conversations I had during the week, just to showcase this workshop from my vantage-point:

  • Jason Cantarella:  Generalize and incorporate derivatives into the notion of particle collisions and compactifications from algebraic geometry.
  • Bob Connelly (one of my mathematical heroes): Incorporate rigidity theory into making every simple polygon evolve into a convex polygon while increasing internal visibility of its vertices.
  • Simon Cox: View the 3D associahedron as the right candidate for the perimeter-minimizing configuration of 9 equal-area bubbles on the sphere.
  • Mohammad Ghomi (a friend from graduate school I have not seen in over 10 years): Relate the linking number to pushing a knot along an injective family of  normal directions.
  • Greg Kuperberg:  Particle collisions with constraints (motivated by Kontsevich) based on a trivalent graph.
  • Wlodek Kuperberg: Show how triangulations on the boundary of a cube induce triangulations of the cube.
  • Frank Morgan: Understand the mission of the MAA Monthly and how to accomplish it better.
  • John Sullivan:  Construct spaces of polygonalizations from a planar point set based on a new set of flip moves.

It was certainly a week to remember, despite the cold.