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Mathematics undergraduate research mentors

Students: if you would like more information, please contact Michael Anshelevich, 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.

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.

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

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.

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
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.

Volodymyr Nekrashevych Combinatorial Group Theory & Functional Analysis.

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.

Guergana Petrova PDE & Approximation Theory, nonlinear approximation, hyperbolic PDEs, conservation laws, numerical quadrature on balls in Rn.

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.

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, elliptic curves, random matrix theory.

2016, 2017, REUs
Igor Zelenko Differential geometry and control theory.

MATH251, MATH308, MATH323 2013, 2014, 2017