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.

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

2014, 2016, 2018  
Michael Brannan  Applications of noncrossing 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  
Riad Masri 
Analytic number theory, automorphic forms, Lfunctions, 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, scattereddata 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 globalscale 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.


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 groupgraded rings.

Math 416 and some form of linear algebra.  2015  
Zhizhang Xie 
Noncommutative geometry, Ktheory, 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, Lfunctions, elliptic curves, random
matrix theory.

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

MATH251, MATH308, MATH323  2013, 2014, 2017 