While it is impossible to give an exact definition of such a vital area as Functional Analysis, its leitmotiv is the amalgamation of algebraic and topological structures: vector spaces endowed with topologies, operators between these vector spaces, and algebras of operators. These structures are found at the core of many fields inside and outside of Mathematics, for example Quantum Physics, Engeneering, Differential Equations, Numerical Analysis. In addition, there are modern day interactions with fields such as Algebraic Topology, Finance, Geometry, Probability and Signal Processing.
Our Functional Analysis group has diverse interests: Banach spaces, operator spaces, C*-algebras, von Neumann algebras, nonlinear functional analysis. Furthermore members of our group are interested in applications to convex geometry, dynamical systems, free probability theory, mathematical finance, mathematical physics, probability theory and wavelets.
Our Linear Analysis Seminar is devoted to the study of several topics in functional analysis, including normed spaces and operators on them, noncommutative theory, and probabilistic methods. Related seminars include the Banach and Metric Space Geometry Seminar, the Free Probabiltiy Seminar, the Groups and Dynamics Seminar, the Noncommutative Functions Seminar the Probabiltiy Seminar and the Several Complex Variables Seminar. The analysis and probability group also organizes the Workshop in Analysis and Probability every summer.