5th Math Colloquium BCAM-UPV/EHU

05 Nov 5th Math Colloquium BCAM-UPV/EHU

Speaker(s): Bernd Sturmfels and Rafael Montenegro

Bernd Sturmfels (Max Plank Institute for Mathematics in the Sciences): “Varieties of Signature Tensors” 
We discuss recent developments in computational algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family we obtain an algebraic variety with interesting properties.

Rafael Montenegro (Institute of Intelligent Systems and Numerical Applications in Engineering): “The Meccano Method for Numerical Simulation”
We present advances of the Meccano method [1,2,3] for tetrahedral mesh generation and volumetric parameterization of solids. The method combines several former procedures: a mapping from the Meccano boundary to the solid surface, a 3-D local refinement algorithm and a simultaneous mesh untangling and smoothing. The key of the method lies in defining a one-to-one volumetric transformation between the parametric and physical domains. Results with adaptive finite elements will be shown for several environmental problems (wind fields, air pollution, solar radiation), see for example [4]. In addition, the application of the method to T-spline modelling and isogeometric analysis [5,6,7] of 3-D geometries will be introduced.