Metric Curvatures and Applications

Metric curvatures represents a minimalistic, foundational approach to the development of a Discrete Differential Geometry on a very general call of geometric objects (spaces).

We survey the essential types of metric curvatures, namely Menger and Haantjes curvatures of curves, and Wald curvature for surfaces, special accent being placed upon the last one. We investigate the relationship between these notions, as well as those with the far better known notion of Alexandrov curvature.

Special accent is placed upon the various applications, both intra-mathematical (Complex Analysis, fractals, construction of Lipschitz functions, metric Ricci curvature for PL cell complexes and a metric Ricci flow for PL surfaces) as well as in "real life" (DNA Microarray Analysis, Protein Folding, Networks, Imaging and Graphics, Wavelets, Pattern Recognition).

Date and time info
Thursday: 11:15 - 13:00

Keywords
Metric Geometry and its Applications

Prerequisites
Basic Mathematical Analyis, rudiments of Differential Geometry (preffered), curiosity and a quest for "real life" applications of "Pure" Mathematics.

Audience
MSc students, PhD students, Postdocs

Language
English

Remarks and notes
These lectures are envisioned, at this stage, as an overview. However, given specific interests of the attendance and/or requests, more technical details can be added, as well as special emphasis/focus on specific areas/subjects. Lecture series will only be offered till December!