Undergraduate Research

Please visit the Mathematics Undergraduate Research page for department wide information about current research opportunities for undergraduate students (including when and how to apply for funding). Below is a snapshot of the undergraduate research being done within the MAC group.

COMAP Mathematical Contest in Modeling

The COMAP Mathematical Contest in Modeling (MCM) is an annual international contest where teams of three undergraduate students use mathematical modeling to solve a real world problem. Teams have just 4 days to choose one of two posed problems, clarify and make necessary assumptions about the problem, develop and analyze a mathematical model, and compose their findings in a clear and coherent paper. A panel of judges then score the solution papers and prizes are awarded. In 2014, 6,755 teams representing institutions from 18 countries competed in the MCM.

The next contest will be held TBA.

The competition is an excellent opportunity to practice and demonstrate your mathematical skills. It’s a rewarding and fun, albeit intense, experience. It also is an impressive resume credential when applying for internships or graduate school. Below are some links to more information.

Informational meeting: TBA. Please contact Braxton Osting (osting AT math DOT utah DOT edu) for more information.

Math 4800 - Introduction to Research

These courses provide a research experience in a familiar course setting. There is usually one Applied Mathematics topic every academic year. Here is a list of topics involving the MAC group since the Fall 2012. The complete list is at the Math 4800 archive page.

Spring 2019. Financial Machine Learning. Instructor: Jingyi Zhu
Spring 2016. Network Inverse Problems. Instructor: Fernando Guevara Vasquez
Fall 2014. An inverse problem: finding boundary fields which produce breakdown. Instructor: Graeme Milton
Spring 2014. Selected Numerical Algorithms and Their Analysis. Instructor: Yekaterina Epshteyn

Research Experience for Undegraduates (REUs)

Here is a list of undergraduates doing research within the MAC group (since Fall 2012).

Fall 2020

Noelle Atkin. Music, ecology, and mathematics. Mentor: Fred Adler
Rebecca Bateman. Mathematical epidemiology. Mentor: Fred Adler
Emma Coates. Extreme first passage times for discrete random walks on networks. Mentor: Sean Lawley
Elijah Counterman. Stochastic pharmacokinetic models. Mentor: Sean Lawley
Tyler Kroll. Practical, and accurate, mathematical function computation. Mentor: Nelson Beebe

Spring 2020

James Eckstein. Numerical Algorithms for the Automatic Processing of Image Data, Specifically Grain Growth. Mentor: Yekaterina Epshteyn
Caeley Lewis. Penrose Tilings and Discrete Structures. Mentors: Andrej Cherkaev and Andrejs Treibergs
Nancy Lyu. Building Optimal Portfolios without Relying on the Inverse of the Covariance Matrix for the Returns. Mentor: Jingyi Zhu
Kayla Stewart. Closing the Gap: How Sea Ice Algae Live or Die within Gap Layers. Mentors: Ken Golden
Jackson Turner. Computation of Eigenfunctions on Various Domains. Elena Cherkaev and Dong Wang

Fall 2019

Emily Coates. Numerical investigation of fluid sloshing with surface tension. Mentors: Christel Hohenegger, Nathan Willis and Chee Han Tan
Camille Humphries. Marble degradation in 2D. Mentors: Yekaterina Epshteyn and Qing Xia
Kayla Stewart. Ding! Exploring the “Dinner Bell” for Algal Blooms. Mentors: Ken Golden
Jackson Turner. Computation of Eigenfunctions on Various Domains. Elena Cherkaev and Dong Wang
Taylor Yates. Extreme Statistics of Diffusios. Mentor: Sean Lawley

Summer 2019

Eric Brown. Reduced-order modeling of Helmholtz equation. Mentor: Fernando Guevara Vasquez
Emily Coates. Numerical investigation of fluid sloshing with surface tension. Mentors: Christel Hohenegger, Nathan Willis and Chee Han Tan
Camille Humphries. Fast Numerical Algorithms for Models with Nonlinear Diffusion. Mentors: Yekaterina Epshteyn and Qing Xia

Spring 2019

Justin Baker. Optimal Transportation Networks. Mentor: Elena Cherkaev
Charlotte Blake. Efficient Numerical Algorithms for Automatically Processing Data with Application to Materials Science. Mentor: Yekaterina Epshteyn
Emily Coates. Numerical investigation of fluid sloshing with surface tension. Mentors: Christel Hohenegger, Nathan Willis and Chee Han Tan
Camille Humphries. Fast Numerical Algorithms for Models with Nonlinear Diffusion. Mentors: Yekaterina Epshteyn and Qing Xia
Gabrielle Legaspi. Coarsening Models. Mentor: Yekaterina Epshteyn

Fall 2018

Justin Baker. Designed Swarming behavior Using Optimal Transportation Networks. Mentor: Elena Cherkaev
Charlotte Blake. Efficient Numerical Algorithms for Automatically Processing Data with Application to Materials Science. Mentor: Yekaterina Epshteyn

Summer 2018

Jack Garzella. Understanding spring network approximations for continuous elastic bodies. Mentor: Fernando Guevara Vasquez

Spring 2018

Charlotte Blake. Approximation of bistable spring chain dynamics. Mentor: Andrej Cherkaev
Jack Garzella. Using spring and mass networks to model an elastic body. Mentor: Fernando Guevara Vasquez
Delaney Mosier. Poisson equation model for sea ice concentration fields in a changing climate. Mentor: Ken Golden

Summer and Fall 2017

Max Carlson. A numerical solution to the free surface sloshing problem with surface tension. Mentors: Christel Hohenegger and Braxton Osting
Peter Harpending. Numerical Fractional Calculus. Mentor: Elena Cherkaev
Alex Henabray. Flow around axisymmetric biconcave shapes. Mentor: Christel Hohenegger
Barrett Williams. Diffusion Equation with Cross-Derivative Term with Variable Coefficients. Mentor: Jingyi Zhu

Spring 2017

Max Carlson. Improving the Numerical Method for Approximating Solutions to the Free Surface Sloshing Model. Mentors: Christel Hohenegger and Braxton Osting
Rebecca Hardenbrook. Bounds on the thermal conductivity of sea ice in the presence of fluid convection. Mentor: Ken Golden
Peter Harpending. The geometry of Fractional Calculus. Mentor: Elena Cherkaev
Michael (Barrett) Williams. Ice Diffusivity. Mentor: Elena Cherkaev

Fall 2016

Peter Harpending. The general solution of fractional-order linear homogeneous ordinary differential equations. Mentor: Elena Cherkaev
Kira Parker. Ranking Methods in Competitive Climbing (Intro to Research). Mentor: Braxton Osting
Caleb Webb. A classical model for infinite, periodic, nonreciprocal media with dissipative elements. Mentor: Maxence Cassier

Summer 2016

Max Carlson. Constructing a Numerical Solution to Sloshing Free Surface using FEniCS. Mentors: Christel Hohenegger and Braxton Osting
Olivia Dennis. Information Theory. Mentor: Braxton Osting

Spring 2016

Tyler McDaniel. Utah’s Pathways to Higher Education: A Quantitive, Critical Analysis. Mentor: Braxton Osting

Fall 2015

Jammin Gieber. Eigenvalues in Chaos. Mentor: Elena Cherkaev

Summer 2015

Jammin Gieber. Deriving the Lorenz equations. Mentor: Elena Cherkaev

Spring 2015

Yuji Chen. The Google rank page. Mentor: Peter Alfeld
Michael Zhao. Spectra of Random Graph Models. Mentor: Braxton Osting
Jeremy Allam. Low-Energy Satellite Transfer from Earth to Mars. Mentor: Elena Cherkaev
Anthony Cheng. Percolation Theory for Melt Ponds on Arctic Sea Ice. Mentor: Ken Golden

Fall 2014

Zhao Jin. Construction of Optimal Portfolio Strategies. Mentor: Jingyi Zhu
Michael Primrose. Imaging with waves in random media. Mentor: Fernando Guevara Vasquez (Supported by NSF DMS-1411577)
Michael Senter. Numerical investigation of First Passage Time through a Fluid Layer. Mentor: Christel Hohenegger (Supported by NSF DMS-1413378)
Wenyi Wang. Imaging in a Homogeneous Aluminum Plate by Using Ultrasonic Waves. Mentor: Fernando Guevara Vasquez
Tao Yu. Construction of Optimal Portfolio Strategies. Mentor: Jingyi Zhu

Summer 2014

Logan Calder. Modeling material failure in a triangular lattice. Mentor: Andrej Cherkaev
Trevor Dick. Nonlinear Elasticity: Optimal Climbing Rope. Mentor: Davit Harutyunyan
Alex Henabray. Numerical Solution of 1D Stefan Problems. Mentors: Yekaterina Epshteyn and Jason Albright
Yang Lou. An extension of the PAM method to three dimensions for interface tracking. Mentor: Qinghai Zhang
Michael Senter. Concurrency and GPU Computing in C++ with MATLAB. Mentor: Christel Hohenegger* Kejia Zhu. Modeling material failure in a triangular lattice. Mentor: Andrej Cherkaev

Spring 2014

Nathan Briggs. General case of 2D and 3D optimal design of optimal composites. Mentor: Andrej Cherkaev
Logan Calder. Fractional Brownian Motion of Prices in the Stock Market. Mentor: Jingyi Zhu
Ryan Durr. The Quantification of Exit Times for varying fluid models. Mentor: Christel Hohenegger
Camille Humphries. Adaptive Numerical Simulation of a 1D Shallow Water Model. Mentors: Yekaterina Epshteyn and Jason Albright
Sage Paterson. Modeling Electrical Breakdown and Fractal Lichtenberg Figures. Mentor: Elena Cherkaev
Michael Primrose. Imaging with waves. Mentor: Fernando Guevara Vasquez
Michael Senter. Numerical investigation of first passage time through a fluid layer. Mentor: Christel Hohenegger
Weny Wang. Uncertainty quantification of acoustic wave propagation in plate material. Mentors: Dongbin Xiu and Fernando Guevara Vasquez

Fall 2013

Nathan Briggs. Optimal three material design on the microstructure and macrostructure scale. Mentor: Andrej Cherkaev
Logan Calder. Fractal Models of Finance. Mentor: Jingyi Zhu
Ryan Durr. The Quantification of Exit Times for Varying Fluid Models. Mentor: Christel Hohenegger
Sophia Hudson. Exploring 2D Truss Structures Through Finite Element Simulation. Mentor: Andrej Cherkaev
Camille Humphries. Adaptive Numerical Simulation of 1D Shallow Water Model. Mentor: Yekaterina Epshteyn
Spencer Phippen. Difference Potentials Method for Interface Problems. Mentor: Yekaterina Epshteyn
Michael Senter. Random Motion in Media with Memory. Mentor: Christel Hohenegger

Summer 2013

Nathan Briggs. Miscrostructure of three wheel assemblages corresponding to extremal conductivity. Mentor: Andrej Cherkaev
Dylan Frank. Damage propagation in lattices. Mentor: Andrej Cherkaev
Camille Humphries. Adaptive Numerical Simulation of 1D Shallow Water Model. Mentor: Yekaterina Epshteyn
Spencer Phippen. Design of the novel numerical method for one-dimensional Stefan problems. Mentor: Yekaterina Epshteyn
Deni Weeks. Wave Chaos - Wave Scarring in Quantum Billiars. Mentor: Elena Cherkaev

Spring 2013

Brady Bowen. Random Fourier Surfaces: Applications to Arctic Melt Pond Modeling. Mentor: Ken Golden
Boya Song. Horizontal fluid transport through Arctic melt ponds. Mentor: Ken Golden
Alessandro Gondolo. Characterization and Synthesis of Rayleigh-damped elastodynamic networks. Mentor: Fernando Guevara Vasquez

Fall 2012

Brady Bowen. Continuum Percolation Model for Melt Pond Evolution. Mentor: Ken Golden
Nick Farrenkopf. The Mass-Spring Cantor Set. Mentor: Elena Cherkaev
Alessandro Gondolo. Mass-Spring networks with damping. Mentor: Fernando Guevara Vasquez
Daniel Khoury. Sea Ice and Electrical Measurements. Mentor: Ken Golden

Webmaster: Fernando Guevara Vasquez. (Created by Yekaterina Epshteyn and FGV)