In this talk I will describe a set of efficient computational methods for analyzing, quantifying and exploring relations and variability in data sets, such as collections of 3D shapes, point clouds, and large networks or graphs, among others. The main unifying theme of this work is that many concepts in data analysis can be considered through the lens of finding relations between real-valued functions using spectral methods. Since real-valued functions can be defined on a wide variety of data representations and, as they enjoy a rich algebraic structure this approach results in both general and efficient computational methods. I will give an overview of these and related techniques and demonstrate, in particular, their use in solving practical problems, including finding both correspondences and differences between 3D shapes.

Maks Ovsjanikov is a Professor at Ecole Polytechnique in France. He received his PhD from Stanford University with an Excellence in Research Award from the Institute for Computational and Mathematical Engineering for his work on spectral methods in shape comparison. He works on 3D shape analysis with emphasis on shape matching and correspondence. He has received a Eurographics Young Researcher Award in 2014 "in recognition of his outstanding contributions to theoretical foundations of non-rigid shape matching". He has served on the technical program committees of international conferences including SIGGRAPH and SIGGRAPH Asia, is a member of the editorial board of Computer Graphics Forum and has co-chaired the Symposium on Geometry Processing in 2016. In 2017 he received an ERC Starting Grant from the European Commission and a Bronze Medal from the French National Center for Scientific Research (CNRS) in 2018.