# Mathematics undergraduate research mentors

Students: if you would like more information, please contact Matt Young, or get in touch with the professor directly. You should still do so even if your desired mentor is not on this list!

Picture | Name and link | Undergraduate research interests Other research interests |
Prerequisites | Recent students | |
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Michael Anshelevich | Orthogonal polynomials ∥ Functional analysis, probability, combinatorics. | Linear algebra and programming experience recommended but not required. | 2012, 2016, 2018 | ||

Gregory Berkolaiko | Spectral problems in mathematical physics. In particular, graph models, their use in physics in general and in the theory of quantum chaos in particular. Combinatorial problems arising in mathematical physics. |
2015, 2016, 2017, 2018 | |||

Harold Boas | Functions of complex variables. |
2016 | |||

Andrea Bonito | Numerical analysis and scientific computation with particular interest in biological systems and fluid dynamics. |
2014, 2016, 2018 | |||

Michael Brannan | Applications of non-crossing combinatorics and linear algebra to problems in operator algebra theory and quantum information theory ∥ Quantum groups, operator algebras, free probability, quantum information theory. |
Linear algebra, some group theory. Some programming skills may be helpful. | 2017 | ||

Goong Chen | Control theory, computational mechanics, partial differential equations, chaotic dynamics, numerical solutions by boundary elements, quantum computation. |
2012 | |||

Andrew Comech | Analysis, partial differential equations, physics. |
MATH 308 or MATH 412 or basic Quantum Mechanics or basic MATLAB skills. | 2015, 2016 | ||

Prabir Daripa | Fluid dynamics, applied mathematics, numerical analysis and scientific computations |
2018 | |||

Tamás Erdélyi |
Polynomials and Polynomial Inequalities. See this course announcement. |
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Stephen Fulling | Mathematical physics, asymptotic and spectral theory of differential operators, semiclassical approximation, quantum field theory in curved space, Casimir energy, pseudodifferential operators. |
Background in physics and differential equations at the approximate level of Math 412. | 2012, 2013, 2014, 2015, 2016, 2017 | ||

Rostislav Grigorchuk | Group theory, dynamical systems, low dimensional topology, discrete mathematics, abstract harmonic analysis, random walks. |
2014 | |||

Jeffrey Kuan | Probability Theory, Representation Theory, Mathematical Physics. |
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Glenn Lahodny Jr | Mathematical epidemiology, mathematical biology, and stochastic processes |
Linear Algebra and Differential Equations. | 2012, 2014, 2015, 2018, REUs | ||

Joseph Landsberg | Geometric questions originating in theoretical computer science, algebraic geometry, differential geometry, exterior differential systems, homogeneous varieties. |
2014, 2017, 2018 | |||

David Larson | Functional analysis, operator algebras, operator theory, frame theory. |
2015, 2018 | |||

Wencai Liu | Spectral theory and inverse spectral theory for discrete Schrödinger operators, Mathematical Physics | Calculus and Linear Algebra. | 2018 | ||

Jonas Lührmann | Partial Differential Equations and Mathematical Physics |
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Riad Masri | Analytic number theory, automorphic forms, L-functions, arithmetic geometry |
2013, REUs | |||

Laura Felicia Matusevich | Combinatorial, algebraic and geometric methods to study hypergeometric functions and differential equations in several variables. |
2015, 2016 | |||

Francis Narcowich | Approximation theory & mathematical physics, radial basis functions, positive definite functions on mainfolds, approximation and interpolation on spheres, quadrature, scattered-data surface fitting, neural networks, and wavelets. |
2015 | |||

Volodymyr Nekrashevych | Combinatorial Group Theory & Functional Analysis. |
2016 | |||

Lee Panetta | Numerical modeling of geophysical flows; numerical simulation of light scattering by atmospheric aerosols; analysis of global-scale atmospheric data. |
2013, 2014 | |||

Joe Pasciak | Large scale parallel scientific computation, numerical and iterative methods for partial differential equations, multigrid and domain decomposition methods. |
2016 | |||

Guergana Petrova | PDE & Approximation Theory, nonlinear approximation, hyperbolic PDEs, conservation laws, numerical quadrature on balls in R^{n}. |
2015 | |||

Eviatar Procaccia | Probability theory. Geometry of random spatial processes, such as percolation, random interlacements and aggregation processes. Random walks on random graphs. |
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Kamran Reihani | Functional analysis, operator algebras, dynamical systems, and noncommutative geometry. |
Some knowledge of linear algebra, programming, and basic modern algebra (e.g., groups and rings) would be helpful. | 2018 | ||

J. Maurice Rojas | Algorithmic algebraic geometry, complexity theory, tropical geometry, polynomial system solving. |
Knowledge of linear algebra, an open mind and an honest desire to learn and do mathematics. | 2012, 2013, 2015, 2017, REUs | ||

Eric Rowell | Braid groups, representation theory, quantum groups and applications to quantum computation. |
Math 415 and some form of linear algebra. | 2014, 2015, 2016, 2017 | ||

William Rundell | Partial differential equations: in particular inverse problems where one has to determine structural elements of the equation from data measurements |
Follow for more details | 2013, 2014, 2015, 2016 | ||

Anne Shiu | Algebraic, geometric, and combinatorial approaches to mathematical biology; biochemical dynamical systems; algebraic statistics; genomics. |
Linear Algebra | 2016, 2017, REUs | ||

Frank Sottile | Computation in algebraic geometry and in combinatorics, and the applications of algebraic geometry. |
Linear algebra and programming experience recommended but not required. | 2012, 2013, 2014, 2016 | ||

Peter Stiller | Algebraic Geometry and Applications of Algebraic Geometry in Robotics, Computer Vision, and Data Analysis. Number Theory, particularly modular forms. |
2013, 2014, 2015 | |||

Edriss Titi | Analysis, control and computational schemes of nonlinear dissipative partial differential equations; turbulence theory, fluid mechanics, oceanic and atmospheric models. |
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Jay Walton | Solid mechanics, mathematical biology and medicine, mechanobiology. |
Previous experience with independent study. | 2012, 2013, 2014, 2015, 2016, 2017, REUs | ||

Sarah Witherspoon | Structure, representations, and cohomology of various types of (noncommutative) rings, including Hopf algebras, quantum groups, and group-graded rings. |
Math 416 and some form of linear algebra. | 2015 | ||

Zhizhang Xie | Noncommutative geometry, K-theory, quantitative linear algebra in geometry and topology ∥ algebraic topology, differential geometry. |
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Guangbo Xu | Differential Geometry related to String Theory | Knowledge of Differential Equations, Topology, or Abstract Algebra (groups); General interest in Geometry or Physics. | |||

Catherine Yan | Algebraic combinatorics, ordered algebraic structures and probabilistic methods. |
2013, 2014 | |||

Philip Yasskin | Applications of computer algebra systems, technology in STEM education. |
2012, 2013, 2014, 2015, 2016 | |||

Matthew Young | Analytic number theory, automorphic forms, L-functions. |
2016, 2017, REUs | |||

Igor Zelenko | Differential geometry and control theory. |
MATH251, MATH308, MATH323 | 2013, 2014, 2017 |