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
	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.
	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.
	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
	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 Rn.			2015
	Eviatar Procaccia	Probability theory. Geometry of random spatial processes, such as percolation, random interlacements and aggregation processes. Random walks on random graphs.
	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.
	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.
	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