Discrete Laplace sequences

Alexander Fairley (TU Berlin)

Tuesday 4th March 16:00-17:00 Maths 311B

Abstract

The talk will be on the discrete differential geometry of conjugate nets with terminating Laplace sequences and thus integrable structure. Conjugate nets are a class of parametrised surfaces. For any conjugate net, Laplace’s cascade method produces a sequence of conjugate nets.  Typically, the sequence is bi-infinite. However, there are interesting cases where the sequence terminates after finitely many steps in one or both directions. The focus will be on terminating Laplace sequences of two types of conjugate nets: curvature-line parametrisations and Koenigs nets. We will compare and contrast new results in the discrete theory to classical results in the smooth theory.

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