I am a Ph.D. candidate in the mathematics department at the University of Nebraska-Lincoln (UNL). I study operator algebras and operator theory with Professor Allan Donsig. Specifically, I study crossed products of operator algebras. The motivation behind crossed product theory is to study symmetries of operator algebras via group actions, which extends the notion of semidirect products and group rings from algebra. Analytically, you can think of crossed product theory as the harmonic analysis of functions on a group that take values in an operator algebra.
I earned a master's degree in mathematics from UNL in 2015 and a bachelor's degree in pure mathematics from Youngstown State University in 2013.
In my free time, I enjoy writing and performing music, communing with nature, and adventuring with my talented partner and our feline companion. The photos on this page were taken during my travels. Enjoy!
In a previous life, I worked as a web developer and programmer. In 2015, I was appointed to lead an initiative to develop resources for the department's online homework system in WeBWorK. My duties included (re)programming the placement and mastery exams for all first-year courses and developing algorithms for workbook randomization. Since then, we have developed a large database of WeBWorK problems and resources to support students in active learning mathematics courses at UNL.
I've included some resources for the "code curious" below. My website theme is a hack of the W3Schools Parallax Theme, which is built on their excellent W3.CSS framework. I highly recommend reading about the W3.CSS framework if you're interested in responsive web design.
I am teaching Math 221/821 Differential Equations during the Spring 2019 semester. (Students, please note that all course materials and policies are available on Canvas.) Below is a list of courses I have taught during my time at UNL.
As an instructor of record, I have taught:
* Indicates courses taught as a co-instructor.
As a teaching assistant, I have taught:
 Wakefield, N., Uhing, K., Hamidi, M., Building Long-Term Support for Faculty through Graduate Student Instructor Professional Development. Smith, W. M., Lawler, B. R., Strayer, J.F., Augustyn, L. (Eds.). (2018). Proceedings of the Sixth Annual Mathematics Teacher Education Partnership Conference. Washington, DC: Association of Public Land-grant Universities.
I co-authored the above peer-reviewed paper with Nathan Wakefield and Karina Kelly in Spring 2018, and it was published in the 2018 Mathematics Teaching Education Partnership (MTEP) Conference Proceedings. Our goal was to detail outcomes of the pedagogical professional development program implemented by the Mathematics Department at University of Nebraska-Lincoln in Fall 2014.
The origins of operator algebras lead back to John von Neumann in the 1920s as he and his co-authors developed a mathematical formalism to the burgeoning field of quantum mechanics. It was determined that observables in a quantum mechanical system, or measurable quantities like position and momentum, should be modeled as self-adjoint operators on the state space of the system, which we call Hilbert space. The “correct” abstract characterization of an algebra of observables is a C*-algebra. Since then, operator algebras have made connections to a wide range of disciplines and can be described in terms of non-commutative ring theory, topology, and measure theory. In particular, the study of C*-algebras has led to significant advancements in group representation theory, knot theory with the Jones polynomial, and ergodic theory. In finite dimensions, operator algebras can be reframed in terms of linear algebra and matrix theory.
My current project characterizes when dynamics on a given operator algebra can be extended to dynamics on C*-algebras. For example, we might be interested on when the action of a group on the upper triangular \(n \times n\) matrices extends to an action of that group on a C*-algebra generated by the upper triangular matrices. Even this finite dimensional case is interesting. I have shown that the collection of all C*-algebras that admit this dynamical extension have a surprisingly rich structure.
Friday, January 18, 2019 at 4:30pm
Room 334, BCC
Mitch Hamidi, University of Nebraska-Lincoln
Get in touch!
You may also find me around Lincoln on a quest for .