Operator Theory/Operator Algebras

Operator Theory and Operator Algebras are concerned with the study of linear operators, usually on vector spaces whose elements are functions. The subject is analysis, but because the vector spaces are usually infinite dimensional, the subject has a nice blend of techniques from other areas of mathematics, ranging from algebra to topology to dynamical systems.

There is a weekly seminar, meeting at 3:30 on Thusdays, and there is a student-run Operator Theory Reading Seminar.

Faculty

Allan Donsig has interests in structural results for nonselfadjoint operator algebras and applications of inverse semigroups to operator algebras. Recent papers are on such topics as coordinatization results, amalgams of inverse semigroups, tight C*-algebras, and describing Cartan MASAs in von Neumann algebras in terms of inverse semgroup extensions. More information, including recent papers, are on Allan's homepage.

David Pitts has interests in coordinatization of operator algebras, operator space theory, free semigroup algebras (a non-commutative analog of analytic functions in several variables) and nest algebras.

Christopher Schafhauser has interest in the structure and classification theory of nuclear (a.k.a. amenable) C*-algebras. Other interests include crossed product C*-algebras, graph C*-algebras, and connections between operator algebras quantum information theory..

Current Graduate Students

Juliana Bukoski
Advised by: Allan Donsig

Catherine Godfrey
Advised by: David Pitts

Sean Gravelle
Advised by: David Pitts

Robert Huben
Advised by: David Pitts and Mark Brittenham

Stephanie Prahl
Advised by: David Pitts

Morgan Swaidan
Advised by: Allan Donsig

Recent Graduates

Derek DeSantis (PhD 2019)
Advised by: David Pitts

Mitch Hamidi (PhD 2019)
Advised by: Allan Donsig

Lara Ismert (PhD 2019)
Advised by: Allan Donsig and David Pitts

Travis Russell (PhD 2017)
Advised by: Allan Donsig

Philip Gipson (PhD 2015)
Advised by: David Pitts

Christopher Schafhauser (PhD 2015)
Advised by: Allan Donsig and David Pitts

Firuz Kamalov (PhD 2011)
Advised by: Allan Donsig

William Grilliette (PhD 2011)
Advised by: David Pitts