Mathematics Colloquium
Upcoming Colloquium
From Hilbert Spaces to Free Products of C*-Algebras
Mícheál Ó Cobhthaigh, Ph.D. candidate, University of Virginia
March 2, 2026
12:30pm-1:30pm in FO3-200A
Abstract
Starting from the familiar setting of bounded operators on a Hilbert space, we introduce C*-algebras as norm-closed *-algebras of operators equipped with a notion of “average” given by a state. We then describe the reduced free product construction, which combines C*-algebras in a way that models a noncommutative form of independence. When certain highly symmetric unitary elements, such as Haar unitaries, are present, these free products exhibit a strong internal symmetry property known as selflessness. I will outline recent results showing that large classes of reduced free products and graph products satisfy this property under natural assumptions.
Biosketch
Mícheál Ó Cobhthaigh is a Ph.D. candidate in mathematics at the University of Virginia, working in operator algebras under the supervision of Ben Hayes. His research focuses on structural properties of C*-algebras arising from free and graph product constructions, including recent work on selfless C*-algebras and group C*-algebras.
About the Colloquium
The Mathematics Colloquium is a unique opportunity for students to learn about new developments in mathematics and what mathematics and statisticians do after they graduate. Hosted by the Department of Mathematics and Statistics at California State University, Long Beach, the weekly meetings invite guests from universities, research laboratories, and industry to present and discuss current topics in mathematics. All students are encouraged to attend.
Schedule
The Spring 2026 schedule will be posted as it becomes available.
| Date | Title | Speaker and Affiliation |
|---|---|---|
| March 2, 2026 | From Hilbert Spaces to Free Products of C*-Algebras | Mícheál Ó Cobhthaigh, University of Virginia |
| March 16, 2026 | TBA | Dr. Dan Rogalski, UC San Diego |
| March 20, 2026 | TBA | Guram Bezhanishvili, New Mexico State University |
| March 24, 2026 | TBA | Dr. Harold Williams, USC |
| April 6, 2026 | TBA | TBA |
| April 13, 2026 | TBA | Dionne Cross Francis, University of North Carolina |
| April 20, 2026 | TBA | Casey Griffin, University of La Verne |
| April 27, 2026 | TBA | TBA |
| May 4, 2026 | TBA | TBA |
Previous Colloquia
| Date | Title | Speaker and Affiliation |
|---|---|---|
| February 9, 2026 | On the squared-variable approach for nonlinear (semidefinite) programming | Dr. Lijun Ding, UC San Diego |
| February 2, 2026 | An Epistemic Reification Approach to Abstracting Cognitively Contingent Scaffolding in Modeling | Dr. Sindura Kularajan, Utah State University |
| January 26, 2026 | Translanguaging in Mathematics: Culturally and Linguistically Responsive Pedagogy | Dr. Adeli Ynostroza Ochoa, CSU Bakersfield |
The Mathematics Colloquium Archive has the colloquia from previous semesters.
Colloquium Committee
For Fall 2025:
- Dr. Pavneet Kaur Bharaj
- Dr. Dan Kaplan
- Dr. Kathryn McCormick
