Molecules are dynamical systems that can adopt a variety of three dimensional conformations which, in general, differ in energy and physical properties. The identification of energetically favourable conformations is fundamental in molecular physics and computational chemistry, since it is closely related to important open problems such as the prediction of the folding of proteins and virtual screening for drug design.
In this talk I will present theoretical and data-driven approaches to the study of molecular conformational spaces and their associated energy landscapes. I will show that the topology of the internal molecular conformational space might change after taking its quotient by the group action of a discrete group of symmetries. I will also show that geometric and topological tools for data analysis such as procrustes analysis, local dimensionality reduction, persistent homology and discrete Morse theory provide with efficient methods to study the mathematical structures underlying the molecular conformational spaces and their energy landscapes.
- Topological Data Analysis Seminar