Here is an evolving list of the projects proposed by mentors for this summer. You do not need to choose a project in your application. The committee will coordinate with mentors and match with students.
Jenia Tevelev: Algebraic Geometry, details can be found at https://websites.umass.edu/tevelev/mentoring/
Leili Shahriyari: Mathematical modeling of bone
Owen Gwilliam, Abstract algebra to tackle problems like matrix models or quantum error correcting codes
Matthew Dobson: Speeding up Markov Chain Convergence - Markov chains are widely used in modeling randomness and as a tool for sampling large data sets. There are many techniques for speeding up the sampling process, and this project will be looking at enhancing the sampling of finite state-space Markov chains using both numerical and analytical approaches.
Weimin Chen: The REU project is concerned with constraints on rational cuspidal curves in the complex projective plane, a classical topic in algebraic geometry. We aim to investigate an alternative approach to this classical problem, which is computer aided and based on tools from symplectic geometry and 4-manifold topology.
Andreas Buttenschoen: Computational biology
Troy Wixson, 1) Neural Bayes Estimators for time series models that are developed to capture the dependence in the tail of the distribution. These models are used, for example, to assess the increased risk of wildfires. 2) Create a map of a county (or state or country) which demonstrates where wildfire risk has increased and by how much. 3) Predict which plant species will be most suitable in different regions across the US conditional on climate change and the presence of invasive species.
Kien Nguyen, The REU project investigates chaotic dynamics and ergodic behavior in planar billiard systems, where a particle moves freely and reflects elastically off curved boundaries. Students will study how geometric features influence hyperbolicity, Lyapunov exponents, and long-term statistical behavior. The project combines analysis of the billiard map with computational experiments to measure finite-time dynamical quantities. Students may also explore parameter dependence and intermittency phenomena in classical chaotic models..
Paul Hacking, Algebraic geometry (study of singularities of plane curves and associated birational geometry of surfaces)
Chris Cox, No-slip Billiards: Billiard dynamical systems, in which particles move freely until colliding with a boundary, have been studied for over a century. The alternative model of no-slip billiards, incorporating angular momentum, has recently been a topic of interest, but many fundamental questions remain open. We will investigate these both analytically and numerically.
Qian Zhao (ds4cg): In this project, you will study how transportation access and local affordability influence food insecurity, nutritional insecurity and health of the population. You will analyze both community level data from County Health Ranking and individual survey data from National Health and Nutrition Examination Survey (NHANES) and Household Pulse survey.