## 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)