Departamentul de Metode şi Modele Matematice

Abstract: We bring into perspective the infamous Riemann zeta function and its natural generalization, the multiple zeta functions. We focus on the evaluations of such objects at positive integers and how they are related to some big conjectures in the field. Although they look rather simple, it turns out that the Riemann zeta and multiple zeta values play a very important role at the interface of analysis, number theory, geometry and physics with applications ranging from periods of "easy" varieties in algebraic geometry to evaluating Feynman integrals in quantum field theory. The talk should be accessible to non specialists and graduate students.

Abstract: During the last 20 years, the interaction of (Algebraic) Topology and Data Analysis moved from a beautiful original ideea to very useful ones with consequences not obtainable by other methods. The purpose of this presentation is to introduce the audience in the mathematics of this interaction which involves linear algebra, combinatorial topology, geometrization of data and in fact much more. The key words in this interaction are: geometrization of point cloud data, computer friendly topological invariants, persistence homology, barcodes, Jordan blocks.