Applied and Interdisciplinary Mathematics
Prof. Vershynin’s main area of expertise is high dimensional probability and its applications. He is interested in random geometric structures that appear in various data science problems. The following is a sample of his recent projects: 1. High dimensional inference from nonlinear data Sometimes we are given certain observations of an unknown vector that encodes useful but hidden information, and we want to compute that vector. Examples includes compressed sensing, linear and non-linear regression, as well as binary (yes-no) observations. We are developing methods that can estimate the hidden vector without even knowing the nature of the non-linearity of observations. Areas of application include survey methodologies, signal processing, and various high-dimensional classification problems. 2. Structure mining in networks Complex data sets such as networks often have latent structures, for example clusters or communities. We are interested in developing efficient methods to discover such latent structures. Prof. Vershynin’s methods come from various areas of mathematics and data science, including random matrix theory, geometric functional analysis, convex and discrete geometry, geometric combinatorics, high dimensional statistics, information theory, learning theory, signal processing, theoretical computer science and numerical analysis.