At the 10th International Summer School on AI and Big Data, Prof. Sayan Mukherjee will talk about A sheaf-theoretic construction of shape space.

Talk: A sheaf-theoretic construction of shape space.

In this talk, we present a sheaf-theoretic construction of shape space—the space of all shapes. Shape spaces are intended to provide a single framework for comparing shapes. Different shapes are rendered as different points in shape space and comparisons of shapes can be formalized in terms of distances between these different points

To study the shape space, we introduce an algebraic construction using a homotopy sheaf on the category of constructible sets, where each set is mapped to its Persistent Homology Transforms (PHT). This algebraic construction of shape space circumvents some of the existing problems in this study area, as topologically different subsets of d dimensional Euclidean space can be viewed simultaneously and compared in this framework.

Bio

Prof. Dr. Sayan Mukherjee his doctorate from MIT, Cambridge, USA, in 2001 and initially stayed there and at the nearby Broad Institute on a Sloan Postdoctoral Fellowship. He has worked at Duke University, Durham, USA, since 2004 and has been a full professor since 2015. He has been associated with several departments as Professor of Mathematics, Applied Statistics and Computer Science. In 2011, he spent a year as a visiting scholar in Chicago. In 2008, he received a Young Researcher Award from the International Indian Statistical Association and has been a Fellow of the Institute of Mathematical Statistics since 2018. He is also a member of various international professional societies.

His research interests are:

• Statistical and computational methodology in genetics, cancer biology, metagenomics, and morphometrics;
• Bayesian methodology for high-dimensional and complex data;
• Machine learning algorithms for the analysis of massive biological data;
• Integration of statistical inference with differential geometry and algebraic topology;
• Stochastic topology;
• Discrete Hodge theory;
• Inference in dynamical systems.