Geometry for data analysis

Antonio Lerario is currently Associate Professor at the International School for Advanced Studies in Trieste, Italy. Thanks to funding from the Knut and Alice Wallenberg Foundation, he will be a visiting professor at the Department of Mathematics, KTH Royal Institute of Technology, Stockholm.

With the recent explosion in the amount and the increasing complexity of available data, understanding and exploiting their underlying structure has become a problem of fundamental importance in the sciences. 

This applied problem is a challenge also for pure mathematics which, over the last years,  developed new methods for analysing data, often presented as clouds of points in a large dimensional space, concentrated near low-dimensional objects, which are not immediately visible.

Unveiling the topological structure of these low-dimensional objects is a central topic of  topological data analysis. The core of the planned project is integrating these methods with real algebraic geometry, viewing the hidden objects as defined by real polynomial equations.

This research will investigate questions at the interface between real algebraic geometry and algebraic topology, with the aim of developing a geometric framework for studying high dimensional data through the geometry of their hidden structures, associating them new invariants using real algebraic geometry.

With the support of the WASP (Wallenberg AI, Autonomous Systems and Software Program) research program, KTH has built up research in mathematics for artificial intelligence and data, in which the group in topological data analysis plays a central role. As a world-leading expert in real algebraic geometry, visiting researcher Antonio Lerario will initiate new joint projects on the mathematical foundations of topological data analysis.