Physical Sciences and Mathematics Commons^™

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science

One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.

First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …

Lines On A Smooth Projective Surface, Jordan Demoura

Mathematics & Computer Science Student Scholarship

Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math

This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.