Algebraic topology meets data science — with applications

Abstract: Many problems in modern data science can be phrased as
topological questions: e.g., clustering is akin to finding the connected
components of a space, and regression/classification can be thought of
as learning maps between structured spaces. I will describe in this talk
how tools from algebraic topology, such as (co)homology and vector
bundles, can be leveraged for the analysis of complex data sets. Several
illustrative examples will be provided, including applications to
computer vision, machine learning and computational biology.

Bio:
Jose Perea is an active researcher in the area of computational topology and topological data analysis. Broadly speaking, his work entails applications and adaptations of ideas from algebraic and geometric topology to the study of high-dimensional and complex data. Perea received his B.S. in mathematics from Universidad del Valle – Cali, Columbia in 2006 (Summa cum laude and Valedictorian), a Ph.D. in mathematics from Stanford University in 2011, and held a postdoctoral position as a visiting assistant professor in the department of mathematics at Duke University (2011 to 2015). In spring of 2014, he was a member of the Institute for Mathematics and Applications at the University of Minnesota, during the annual thematic program on scientific and engineering applications of algebraic topology.