Functional Analysis, Operator Theory and Operator Algebras

Operator theory, linear systems, optimal control

Systems and control theory, operator theory in Hilbert spaces, module theory and linear algebra

Topological groups (general theory), abstract harmonic analysis, topological dynamics

Operator theory, functional analysis, matrix theory.

Complex analysis, spectral theory of differential operators, functional equations.

Operator theory, system theory, algebraic geometry

Free Analysis, Operator Theory, Complex Analysis

operator algebras, noncommutative convexity, function theory, several complex variables, real and complex algebraic geometry

I work in the intersection between group dynamics and operator algebras. Most of my PhD work was devoted to understanding the structure of the crossed product structure.

Here are some(or all) of my publications:

1. Generalized Powers’ averaging for Commutative crossed products., to appear in Transactions of the American Mathematical Society, preprint available at arXiv:2101.02853 ; (Joint with Dan Ursu).

2. On Intermediate C-subalgebras of C-simple Group Actions, International Mathematics Research Notices, Volume 2021, Issue 21, November 2021, Pages 16191–16202, https://doi.org/10.1093/imrn/rnz291, preprint available at arXiv:1811.11381.

3. On simplicity of intermediate C*-algebras, Ergodic Theory and Dynamical Systems, 40(12), 3181-3187. doi:10.1017/etds.2019.34 ; (Joint with Mehrdad Kalantar)

Operator algebras

Operator algebras.

Geometric analysis: Sobolev spaces theory. Quasiconformal analysis. Geometric measure theory. Analysis on metric measure spaces.