# Curves

Monday, June 17, 2019 - 11:30am - 12:30pm

Peter Schroeder (California Institute of Technology)

Differential geometry has historically been conceived and studied in the smooth setting. Much can be learned this way. Yet, when it comes to computation and the many problems and questions which can only be accessed through computation we must leave the ideal world of infinitely differentiable objects and descend to the finite dimensional world a computer can deal with. Thus enters Discrete Differential Geometry. What are appropriate notions of, for example, curvatures in the discrete setting of polylines of triangle (surface) meshes?

Tuesday, June 25, 2019 - 9:00am - 10:00am

Soeren Bartels (Albert-Ludwigs-Universität Freiburg)

We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of a bending energy and a so-called tangent-point functional. We define evolutions via the gradient flow for the total energy within a class of arclength parametrized curves, i.e., given an initial curve we look for a family of inextensible curves that solves the nonlinear evolution equation.

Wednesday, February 12, 2014 - 10:15am - 11:05am

Sigurd Angenent (University of Wisconsin, Madison)

Curves that evolve under Curve Shortening by a combination of rescaling and Euclidean motions are solutions to a system of ordinary differential equations on the unit tangent bundle of Rn.

The flow, which has no fixed points, does admit an interesting Morse decomposition, especially after compactifying the phase space.

In this talk I will present the many different solutions to Curve Shortening that arise in this way.

The flow, which has no fixed points, does admit an interesting Morse decomposition, especially after compactifying the phase space.

In this talk I will present the many different solutions to Curve Shortening that arise in this way.

Monday, January 30, 2012 - 11:15am - 12:15pm

Mark Behrens (Massachusetts Institute of Technology)

In response to a question of Milnor, a collaboration of Mike Hill, Mike Hopkins, Mark Mahowald, and myself have been attempting to determine in which dimensions exotic spheres exist. We will review