# Mitch Hamidi

Office: 344 Avery Hall (map)

Email: mhamidi [at] huskers.unl.edu

Office Hours: M 3:00-4:00pm, W 1:00-2:00pm, and by appointment.

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.

### The Mountains are Calling and I Must Go...

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!

### Code Wizard

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.

### Programmer's Toolbox

• UNL Math Grad Theme 1.0 - A starter theme for the UNL Math Grad student. Feel free to change what you like. Enjoy.
• UNL Web Developer Network - Some nifty tools for the UNL web developer. Their color palette inspired this page.
• W3 Schools - A great resource for syntax and basic web programming knowledge. From HTML to server-side scripting, it's all here.
• Code Academy - Free coding exercises for several programming languages. If you're interested in learning a new programming language, this is a great place to start!

HTML & CSS

C++

Python

Matlab
TEACHING

### MY TEACHING

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:

• Math 806T Number Theory and Cryptology for Middle Level Teachers (Summer 2015)*
• Math 800T Mathematics as a Second Language for Middle Level Teachers (Summer 2016)*
• Math 314/814 Linear Algebra (Summer 2017, Spring 2017)
• Math 301 Geometry Matters (Spring 2016)
• Math 300 Mathematics Matters (Fall 2015)
• Math 221/821 Differential Equations (Spring 2019)
• Math 208 Calculus III Multivariate/Vector Calculus (Fall 2017)
• Math 106 Calculus I (Fall 2018, Fall 2016)
• Math 104 Applied Calculus (Summer 2018)
• Math 102 Trigonometry (Spring 2015, Summer 2014)
• Math 101 College Algebra (Spring 2018)
• Math 100A Intermediate Algebra (Fall 2014)

* Indicates courses taught as a co-instructor.

As a teaching assistant, I have taught:

• Math 106R Calculus I Recitation (Fall 2018, Fall 2016, Spring 2014, Fall 2013)

### Teaching Publications

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.

RESEARCH

### Foundations of Operator Algebras

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.

### Current Research

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.

I am chairing a session and presenting my work at the Joint Mathematics Meetings in Baltimore, MD at 4:30pm on Friday, January 18, 2019. Details for my talk are below. Stop by and say hello!

Friday, January 18, 2019 at 4:30pm

AMS Contributed Paper Session on Operator Theory

Room 334, BCC

Admissibility of C*-Covers and Crossed Products of Operator Algebras