### Algebra

, Professor*Reza Akhtar*

Algebraic Geometry, K-theory, Combinatorics, Assistant Professor**Jason Gaddis**

Noncommutative Algebra, Associate Professor**Dennis Keeler**

Algebraic Geometry, Noncommutative Rings

Find faculty who are working in specific areas of research.

, Professor*Reza Akhtar*

Algebraic Geometry, K-theory, Combinatorics, Assistant Professor**Jason Gaddis**

Noncommutative Algebra, Associate Professor**Dennis Keeler**

Algebraic Geometry, Noncommutative Rings

, Professor*Patrick Dowling*

Functional AnalysisAssociate Professor*Caleb Eckhardt,*

Operator Algebras, Professor*Beata Randrianantoanina*

Functional Analysis, Professor**Narcisse Randrianantoanina**

Functional Analysis

, Professor*Anna Ghazaryan*

Applied analysis, ordinary and partial differential equations, applied dynamical systems, nonlinear waves, Associate Professor (Hamilton Campus)*Vahagn Manukian*

Applied analysis, applied dynamical systems, existence and stability of traveling waves, Associate Professor*Alin Pogan*

Applied Analysis and Partial Differential Equations, Associate Professor*Alim Sukhtayev*

Applied Analysis, Operator Theory, and Partial Differential Equations

, Professor**Louis DeBiasio**

Extremal/Probabilistic Graph Theory, Professor**Tao Jiang**

Graph Theory, Extremal Combinatorics, Professor**Zevi Miller**

Graph Theory, Combinatorics, Complexity Theory, Professor**Daniel Pritikin**

Graph Theory, Combinatorics, Recreational Mathematics

, Professor**Dana Cox**

Mathematics Curriculum and Student Learning, Professor*Suzanne Harper*

Technology in Mathematics Education, Professor**Jane Keiser**

Geometric student thinking, helping students obtain computational fluency, and professional development partnerships, Assistant Professor**Wayne Nirode**

Teaching and Learning of Geometry

, Associate Professor (Middletown Campus)**Champike Attanayake**

Computational and Financial Mathematics, Associate Professor*Olga Brezhneva*

Optimization, Ordinary Differential Equations, Associate Professor (Hamilton Campus)*Jae Woo Jeong*

Applied and Computational Mathematics, GFEM, Associate Professor*Ebrahim Sarabi*

Variational Analysis and Optimization, Professor*Douglas Ward*

Variational Analysis

, Associate Professor*Tetsuya Ishiu*

Set theory, Professor**Paul Larson**

Set theory, Associate Professor**Trevor Wilson**

Set theory

, Emeritus Professor*Dennis Burke*

Set-theoretic topology, Associate Professor*Daniel Farley*

Geometric Topology, Geometric Group Theory, Professor*Ivonne Ortiz*

Algebraic and geometric topology

There are a plethora of opportunities for mathematics students to become involved in undergraduate research at Miami University. Many of our faculty have been, or currently are, actively engaged in research with students.

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.

Mathematics 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.

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.

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).

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.

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.

Mathematics students at Miami University are actively involved in research projects with our faculty, and through REU programs. Below are some papers from our students. Student names are in bold and faculty mentor(s) in italics.

*Jason Gaddis* and **Thomas Lamkin**. Centers and automorphisms of PI quantum matrix algebras. To appear in *Geometric and Algebraic Aspects of Quantum Groups and Related Topic (AMS Contemporary Mathematics)*.

*Tao Jiang*, **Sean Longbrake**, and Jie Ma. Bipartite-ness under smooth conditions. To appear in *Combinatorics, Probability, and Computing*.

**Jacob Barahona Kamsvaag** and *Jason Gaddis*. Auslander's Theorem for dihedral actions on preprojective algebras of type A. Published in *Canadian Mathematical Bulletin*, 2023, 66 (1), 324-339.

**Milena Brixey** and *Ryan M. Causey*. Uniform upper estimates and the repeated averages hierarchy. Published in *Journal of Mathematical Analysis and Applications*, 2023, Volume 520 (1), 126871.

**Marzieh Bakhshi**, *Anna Ghazaryan*, *Vahagn Manukian*, Nancy Rodriguez. Traveling wave solutions in a model for social outbursts in a tension-inhibitive regime. Published in *Studies in Applied Mathematics*, 2021, 2, 650–674.

**Milena Brixey**, *Ryan M. Causey*, **Patrick Frankart**. Uniform subsequential estimates on weakly null sequences. Published in *Involve*, 2021, 14 (5), 743–774.

*Louis DeBiasio* and **Nicholas Spanier**. On Hamiltonian cycles in balanced k-partite graphs. Published in *Discrete Mathematics*, 2021, 344 (11), 112583.

*Louis DeBiasio*, Yigal Kamel, **Grace McCourt**, and Hannah Sheats. Generalizations and strengthenings of Ryser's conjecture. Published in *Electronic Journal of Combinatorics*, 2021, 28 (4), P4.37, 58pp.

*Louis DeBiasio*, **Robert A. Krueger**, Dan Pritikin, and **Eli Thompson**. Hamiltonian cycles in k-partite graphs. Published in *Journal of Graph Theory*, 2020, 94 (1), 92-112.

*Louis DeBiasio*, András Gyárfás, **Robert A. Krueger**, Miklós Ruszinkó, and Gábor N. Sárközy. Monochromatic balanced components, matchings, and paths in multicolored complete bipartite graphs. Published in *Journal of Combinatorics*, 2020, 11 (1), 35-45.

*Louis DeBiasio*, **Robert A. Krueger**, and Gábor N. Sárközy. Large monochromatic components in multicolored bipartite graphs. Published in *Journal of Graph Theory*, 2020, 94 (1), 117-130.

*Louis DeBiasio* and **Robert A. Krueger**. Long monochromatic paths and cycles in 2-colored bipartite graphs. Published in *Discrete Mathematics*, 2020, 343 (8), 111907.

*Jason Gaddis* and **Phuong Ho**. Fixed rings of quantum generalized Weyl algebras. Published in *Communications in Algebra*, 2020, 48 (9), 4051-4064.

**Benard A. Neuhaus** and *Douglas E. Ward*. Characterizing the contingent cone's convex kernel. Published in *Pure and Applied Functional Analysis*, 2020, 5 (3), 653–669.

Louisa Catalano, Samuel Hsu, **Regan Kapalko**. On maps preserving products of matrices. Published in *Linear Algebra and its Applications*, 2019, 563, 193–206. (Kent State REU)

**Hong Cai**, *Anna Ghazaryan*, and *Vahagn Manukian*. Fisher-KPP dynamics in diffusive Rosenzweig-MacArthur and Holling-Tanner models. Published in *Mathematical Modelling of Natural Phenomenon*. Special issue on Singular perturbations and multiscale systems, 2019, 14 (4).

Samuel Audino, **Delaney R. Aydel**, *Daniel Farley*. Quasiautomorphism groups of type F∞. Published in Algebraic & Geometric Topology, 2018, 18 (4), 2339–2369.

**Clayton Collier-Cartaino**, **Nathan Graber**, and *Tao Jiang*. Linear Turan numbers of r-uniform linear cycles and related Ramsey numbers. Published in *Combinatorics, Probability, and Computing*, 2018, 27, 358-386.

**Axel Brandt**, **David Irwin**, and *Tao Jiang*. Stability and Turan numbers of a class of hypergraphs via Lagrangians. Published in *Combinatorics, Probability, and Computing*, 2017, 26, 367-405.

**Andrew Newman** and *Tao Jiang*. Small dense subgraphs of a graph. Published in *SIAM Journal on Discrete Mathematics*, 2017, 31, 124-142.

**Stephen Colegate** and **Charlie Liu**. Mathematical Modeling of drug use: the dynamics of mono- substance dependence for two addictive drugs. Published in *Pi Mu Epsilon Journal*, 2017, 14 (7), 449-462. (Faculty advisor: *Anna Ghazaryan*)

**Robert Doughty** and **Eli Thompson**. Mathematical Analysis of Ivermectin as a Malaria Control Method. Published in *SIAM Undergraduate Research Online*, 2016, 9. (Faculty advisor: *Anna Ghazaryan*)

**Robert Doughty**, Jessica Gonda, Adriana Morales, Berkeley Reiswig, Josiah Reiswig, Katherine Slyman, *Daniel Pritikin*. Arranging kings k-dependently on hexagonal chessboards. Published in *Involve*, 2016, 9 (4), 699–713.

**Teng Zhang** and **Son Van**. A study of a debt-influenced equilibrium of the Keen model. Published in *Pi Mu Epsilon Journal*, 2016, 14 (4), 275-281. (Faculty advisor: *Anna Ghazaryan*)

*Reza Akhtar*, **Maxwell Forlini**. The linear chromatic number of a Sperner family. Published in *Discrete Applied Mathematics*, 2014, 171, 1–8.

Zoltan Furedi, *Tao Jiang*, and **Robert Seiver**. Exact solution of the hypergraph Turan problem for k-uniform linear paths. Published in *Combinatorica*, 2014, 34, 299-322.

*Reza Akhtar*, Ashley Arp, Michael Kaminski, Jasmine Van Exel, Davian Vernon, **Cory Washington**. The varieties of Bol-Moufang quasigroups defined by a single operation. Published in *Quasigroups and Related Systems*, 2012, 20 (1), 1–10.

*Tao Jiang* and **Robert Seiver**. Turan numbers of subdivided graphs. Published in *SIAM Journal on Discrete Mathematics*, 2012, 26, 1238-1255.

**Edward Boehnlein** and *Tao Jiang*. Set systems with a forbidden induced subposet. Published in *Combinatorics, Probability, and Computing*, 2012, 21, 496-511.

*Tao Jiang* and **Michael Salerno**. Ramsey numbers of some bipartite graphs versus complete graphs. Published in *Graphs and Combinatorics*, 2011, 27, 121-128.

**Katherine E. Strauss**. Investigating Centers of Triangles: The Fermat Point. *Thesis, Miami University*, 2011. (Faculty advisor: *Suzanne Harper*)

**Josh M. Beal**, Amit Shukla, *Olga A. Brezhneva*, Mark A. Abramson. Optimal sensor placement for enhancing sensitivity to change in stiffness for structural health monitoring. Published in *Optimization and Engineering*, 2008, 9, 119–142.

*Zoltan Balogh*, **John Griesmer**. On the multiplicity of jigsawed bases in compact and countably compact spaces. Published in *Topology and its Applications*, 2003, 130 (1), 65–73.

*Dennis K. Burke*, **Justin Tatch Moore**. Subspaces of the Sorgenfrey line. Published in *Topology amd its Applications*, 1998, 90 (1-3), 57–68.

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301 S. Patterson Ave.

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