My research interests have always been primarily in analysis, and are usually in and around the fields of operator algebras and operator theory.
Currently I am involved with projects on
- Multivariable operator theory (dilation theory, matrix ranges and matrix convexity, model theory, noncommutative function theory, noncommutative varieties)
- Completely positive maps and semigroups (interpolation of CP maps, dilations, product systems, superprodcut systems and subproduct systems, C* and von Neumann correspondences)
- Operator systems, non-selfadjoint operator algebras and C*-algebras (algebras of noncommutative functions, abstract dilation theory, C*-envelopes, hyperrigidity, isomorphisms)
- Hilbert spaces and algebras of holomorphic functions (classical as well as noncommutative) and operators that act on them (RKHS, multiplier algebras)
The main line of research I do currently is supported by the following research grants:
- ISF Research Grant No. 431/20 (2020 — 2024) proposal.
Here is a Research Statement, summarizing the central themes of my research up to June 2017.
Here is a Research Report prepared for the workshop “Hilbert Modules and Complex Geometry”, in Oberwolfach, April 2014.
Previous research grants:
- ISF Research Grant No. 195/16 (2016 — 2020) proposal.
- GIF Research Grant No. 2297-2282.6/201 (2013) proposal abstract.
- The Gerald Schwartz & Heather Reisman Foundation for Technion-UWaterloo cooperation (2015 – 2016).
- ISF Research Grant No. 474/12 (2012 — 2016) proposal abstract.
- Marie-Curie CIG Grant No. 321749 (2012—2016) proposal.