The Department of Mathematical Sciences is proud to announce that Rongjie Lai, assistant professor of mathematical sciences, has received a prestigious Faculty Early Career Development Award (CAREER) from the National Science Foundation (NSF).  He will use the five-year, $400,000 award to study "Geometry and Learning for Manifold-Structured Data in 3D and Beyond."

The CAREER Award is given to faculty members near the beginning of their academic careers, and is one of the most competitive awards given by NSF to early-career faculty.  The award recognizes excellence in research as well as plans for novel educational initiatives.

The central focus of Professor Lai's project involves processing and analyzing data is three and higher dimensions.  Such data sets arise in diverse fields such as medical imaging, computational chemistry, computational biology, social networks, among others, and is commonly associated with certain coherent and nonlinear structure.  Mathematically, this allows Professor Lai's group to model data sets as points sampled on manifolds usually of low dimensions embedded in a high dimensional ambient space.  Different from image and signal processing which handle functions on flat domains with well-developed tools for processing and learning, manifold-structured data is far more challenging due to their complicated geometry.  For example, the same geometric object can take very different coordinate representations due to the variety of embeddings, transformations or representations.  These ambiguities form an infinite dimensional isometric group and make higher-level tasks in manifold-structured data analysis and learning even more challenging.  To overcome these challenges, Professor Lai and his students aim to investigate analyzing and learning of manifold-structured data by connecting recent developments in geometric partial differential equations (PDEs) and learning theory to intrinsic data analysis.

Professor Lai received his Ph.D. in mathematics at UCLA.  He held postdoctoral appointments at USC and UC Irvine, before joining the Department of Mathematical Sciences at Rensselaer in August, 2014.  The NSF CAREER award speaks highly of Professor Lai's achievements to date, and the department is fortunate to have him on its faculty.