Università Roma Tre

Brief introduction to Julia language for scientific computing. Intro to geometric modeling and scientific visualization. Simplicial, cellular and chain complexes. Boundary and coboundary operators. Algebraic operators of incidence and adjacency. Duality. Extraction of geometric models from 3D imaging. Delaunay triangulations and Voronoi complexes. Morse functions and Reeb graphs. Elements of topological structures on big data. Persistent homology. Matrix operations and dense linear systems: outline of BLAS, LAPACK, scaLAPACK. Sparse linear systems. CombBLAS, GraphBLAS. Development of a collaborative project.

Herbert Edelsbrunner and John Harer, Computational Topology. An Introduction, AMS, 2011.