Upcoming REU Summer 2020

Patterns and PDEs (2020)

Stripes

We are organizing a summer REU program, to be held at the Mathematical Institute at Leiden University in The Netherlands. We are seeking motivated undergraduate students to spend 6 weeks between June 15, 2020 and July 24, 2020 in Leiden, to work on research related to nonlinear waves and pattern formation, using the theory of dynamical systems and partial differential equations. Applications include vegetation pattern formation and other topics in mathematical biology and ecology.

See the program flyer for additional information.

Faculty mentors: Paul Carter (University of Minnesota), Arjen Doelman (Leiden University)
Application deadline: February 14, 2020
Apply at: MathPrograms.org

Past REU Projects

Stellar winds (2019)

Stellar wind

In the setting of viscous stationary spherically symmetric equations of gas dynamics, we are interested in the existence of sub-to-supersonic transitions which describe the phenomena of stellar wind and stellar accretion. These transitions arise as canard solutions in an appropriate fast-slow framework and can be constructed using geometric singular perturbation theory. In this project, we analyzed the effects of viscosity and heat conduction on the structure of stellar winds.

REU Students: Adam Bauer

Publications:

Localized roll patterns (2016)

Moebius

In a project hosted by the Summer@ICERM program in 2016, groups of undergraduate students studied snaking localized roll patterns in the Swift-Hohenberg equation. They analyzed the effect of the underlying geometry/topology of the equation on the structure of the associated snaking curves, as well as implications for higher dimensional patterns.

Collaborators: T. Aougab, M. Beck, J. Bramburger, B. Sandstede
REU Students: Dylan Altschuler, Chloe Avery, Surabhi Desai, Tharathep Sangsawang, Melissa Stadt, Aric Wheeler

Publications:

Traffic flow (2014)

In this REU project, undergraduate students studied the application of data assimilation to models of traffic flow. In particular, a framework was developed to assimilate both Eulerian (fixed sensor) and Lagrangian (GPS) observations in order to predict traffic states and estimate model parameters.

Collaborators: B. Sandstede, L. Slivinski, C. Xia
REU Students: Courtney Cochrane, Joseph DeGuire, Bridget Fan, Emma Holmes, Melissa McGuirl, Patrick Murphy, Jenna Palmer

Publications: