Event
Yann Rollin, Universit茅 de Nantes
Discrete geometry and isotropic surfaces.
We consider smooth isotropic immersions from the 2-dimensional torus into R2n, for g>=2. When n = 2 the image of such map is an immersed Lagrangian torus of R4. We prove that such isotropic immersions can be approximated by arbitrarily C0-close piecewise linear isotropic maps. If n >= 3 the piecewise linear isotropic maps can be chosen so that they are piecewise linear isotropic immersions as well. The proofs are obtained using analogies with an infinite dimensional moment map geometry due to Donaldson. As a byproduct of these considerations, we introduce a numerical flow in finite dimension, whose limit provide, from an experimental perspective, many examples of piecewise linear Lagrangian tori in R4.