Math department announces spring 2024 Undergraduate Research Award winners

LAWRENCE — The University of Kansas Department of Mathematics has awarded Undergraduate Research Awards in Mathematics (MathUGRA) to three mathematics majors to support their research projects for the spring 2024 semester.

MathUGRAs are $1,000 scholarships provided to undergraduate majors pursuing original research or creative projects under the general guidance of a KU mathematics faculty member.  The awards are provided by the department’s endowment funds.

MathUGRAs are awarded to students conducting semesterlong independent projects culminating in an oral presentation or written work, demonstrating the student’s own development of a topic in mathematics and its applications. Recipients of the award were selected on the merit of the applicant's proposal, the applicant's academic record and the recommendation from a faculty member.

The spring 2024 recipients:

Andrew Lin, Overland Park junior in mathematics: “Invariants of Modules and Ideals in Two-Dimensional Regular Local Rings.” This is a study of algebraic properties over two-dimensional regular local rings focusing on polynomial rings in two variables.  There are many results which, in various cases, compute the ideal K. However, there is no general algorithm for computing the generating set of K; even in specific cases, such algorithms do not guarantee that the generating set is indeed minimal. The goal is to expand on previous research to find a minimal generating set of K under weaker assumptions (relative to previous research). Lin’s research mentor is Hailong Dao, professor of mathematics.

Yash Prajapati, Gujarat, India, junior in mathematics and interdisciplinary computing: “Enhancing Stock Market Predictions Through Machine Learning Techniques: A Comparative Analysis of SVM and Probabilistic Regression Techniques Based Models.” This study will compare support vector machines (SVMs) and linear regression using different features and determine which of these techniques could best be used to analyze and predict future market prices. Prajapati plans to implement his research into an actual bot that is trained on the same techniques mentioned in the proposal to make trades and thus could be evaluated on its performance. Prajapati’s research mentor is Erik Van Vleck, professor of mathematics.

Jackson Torok, Omaha, Nebraska, senior in mathematics and aerospace engineering: “Capturing Shocks in Non-linear Conservation Laws.” Capturing shock dynamics and interactions is critical for studying certain phenomena that appear in real-world situations like Mach diamonds, detonation shocks, shock ingestion, shocks on control surfaces and many more outside of aerodynamics such as Cherenkov radiation. This research seeks to develop two methods that provide accurate shock dynamics for nonlinear conservative systems. Torok’s research mentor is Yannan Shen, associate professor of mathematics.