Roman Vershynin | Research Interests
I work primarily in geometric functional analysis, exploring connections among functional analysis, convex geometry and probability theory. Some of my work extends to probability, geometric combinatorics, convex and discrete geometry, harmonic analysis, theoretical computer science and numerical analysis.

Geometric functional analysis strives to understand and use high dimensional structures in mathematics. High dimensions often have srong regularization effect and help us to see the overall picture. While counter-intuitive, this is very similar to the methodology of probability theory. Taking more independent observations, we increase the dimension of the (product) probability space. As the dimension grows to infinity, the classical limit theorems such as the Central Limit Theorem begin to manifest themselves. The picture becomes simpler in higher than in lower dimensions.

Techniques of geometric functional analysis are useful to explore, build, or use various high-dimensional structures such as Banach spaces, convex sets, matrices, signals and other massive data sets.
 Research

For more detailed discussion of my research, see my publications by topic and commentary. Also visit my webpage at UC Davis.
The material presented at this web site is based upon work supported by the Alfred P. Sloan Foundation and the National Science Foundation under grants DMS 0401032 and DMS 0652617. Any opinions, findings and conclusions or recomendations expressed in this material are those of the author and do not necessarily reflect the views of the granting agencies.