IntroductionThis course will discuss topological modelling of combinatorial objects such as (di-)graphs and hypergraphs. The course will guide the students to read the relevant references on the topic for learning how to apply the theories in algebraic topology to the combinatorial objects. The course will also display some applications of algebraic topology in data analytics through topologica...
IntroductionThis course is an introduction to the convergence and collapsing theory of Riemannian manifolds, which is an important tool in Riemannian geometry. We shall introduce the Gromov-Hausdorff distance and study the convergence theory of Riemannian manifolds with respect to this distance. We will discuss the collapsing theory of Riemannian manifolds with bounded sectional curvatures.Lect...
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