Research interests: image and shape analysis, machine learning, Computational geometry, stochastic process, optimal transport, cryo-EM, gene expression

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Lectures during the School

Lecture 1: Introduction to metrics for biological shape analysis and dimensionality reduction

I will introduce how concepts of Riemannian geometry for representing 2D and 3D shape space provides a natural framework to study cell morphological heterogeneity. The lecture will introduce to the basic concepts of Riemannian geometry through the classical definition of the Kendall shape space, before focusing on quantifying cancer cell morphological variations under various drug treatment using elastic metrics on curves with the Geomstats Python package

Lecture 2: Introduction to Optimal Transport, Wasserstein metrics and application to protein and cell shapes (Wenjun Zhao)

Recent advances in cryogenic electron microscopy (cryo-EM) and tomography (cryo-ET) have allowed to image proteins and biomolecular complexes at an unprecedented resolution, fueling initiatives for cryo-EM guided drug design, including in cancer therapeutics. In this context, I will present the basics of cryo-EM/ET and mathematical challenges associated with it. I will then present and show how variants of the Wasserstein distances arising from Optimal Transport theory can be leveraged to improve current methods in 3D alignment and atomic model building

Lecture 3: Mathematics of 3D shape reconstruction for cryo-EM and cryo-ET