# Undergraduate Research Opportunities

There are a plethora of opportunities for mathematics students to become involved in undergraduate research at Miami University. The Office of Research for Undergraduates offers several research programs, including the Undergraduate Research Award Program and the Undergraduate Summer Scholars Program. The American Mathematical Society maintains a list of summer research programs in Mathematics.

Many of our faculty have been, or currently are, actively engaged with students in research with students. Students who are interested are encouraged to speak directly with our faculty, or may contact Dr. Jason Gaddis (gaddisj@miamioh.edu) for assistance in placement.

**Louis DeBiasio:** My research is in graph theory (where a graph is just an abstract "network"). I specifically work on problems of an extremal, probabilistic, or Ramsey-theoretic nature. A student looking to do research in graph theory should at the minimum take MTH 438.

**Jason Gaddis:** I study a branch of abstract algebra, called noncommutative algebra, where we do not assume that the "ordinary" rules of multiplication are followed. I am especially interested in questions related to symmetry in this setting, but my work instersects with other areas such as representation theory, combinatorics, and algebraic geometry. My personal research website has more information on projects by my former students. I welcome students at all level, but I prefer that students have first completed MTH 421 (Intro to Abstract Algebra).

**Anna Ghazaryan:** My current research is about equilibrium states and traveling waves. Equilibrium states are states preferred by the underlying physical system. For example, the state where a population of a town is healthy and nobody is sick is an equilibrium state. Traveling waves capture propagation of certain property. For example, a combustion wave is a transition from the equilibrium state where there is no fire, to an equilibrium where all or some of the fuel is gone - like in a field or forest fire. Traveling waves arise in problems from different fields: optical communication, combustion theory, biomathematics, chemistry, social sciences to name a few. This area of research requires some background knowledge in Linear Algebra and Differential Equations. Some of my projects are theoretical and some have a computational component.

**Tetsuya Ishiu:** I am interested in giving formal proof (i.e. computer-verifiable proof) to basic statements in mathematics with students. You may want to pass MTH 231 or MTH 331 as the fundamental knowledge about proofs is necessary.