Remus Nicoara Professor and Director of Honors and Research UTK Mathematics

Remus Nicoara  Research In the 1930's, John von Neumann
discovered that certain algebras of operators on a Hilbert space are the
natural framework for understanding symmetries of
quantum physical systems. His ideas play an important
role in quantum mechanics, and fundamental laws of
nature such as the Heisenberg uncertainty principle
appear as a natural consequence of von Neumann's
abstract theory.
My main research
interest lies in the study of subfactors, especially
through their algebraiccombinatorial invariants such
as the socalled commuting
squares. These are squares of inclusions of
finite dimensional C*algebras that arise naturally in
the standard invariant of a subfactor. Commuting
squares can also be used as construction data for
subfactors, and the most explicit examples of
subfactors have been obtained this way. A
particular class of subfactors arises from the
socalled spin
models, which are commuting squares based on
complex Hadamard
matrices. In the recent years Hadamard
matrices have found applications in several areas of
mathematics and physics, such as quantum information
theory, operator algebras, error correcting codes,
spectral sets and Fuglede's conjecture.
