Project Leader Venkata Raghu Tej Pantangi, University of Lethbridge Mahsa N Shirazi, University of Manitoba Graduate Mentor Junaid Hasan, University of Washington Undergraduate Team Members Jaskaran Singh, University of Manitoba Anu Singh, University of Saskatchewan Problem Statement The Smith Normal Forms (SNF) of an incidence matrix is a powerful invariant that may help distinguish the underlying incidence structure.

In this project, students will develop techniques from knot theory and combinatorics to address questions about the geometry and topology of 3-stranded polymers such as R-loops. An R-loop is a 3 stranded structure composed of a DNA-RNA complex and another single strand of DNA.

In this project, students will carry out computations of the number of prime factors of integers and compare the results to theoretical predictions of their relative frequencies.

In this project students will work with large scale genomic data to extend a machine learning model for prediction of multiple cognitive outcomes related to Alzheimer’s Disease.

This project develops a fundamental tool for representation theory of p-adic groups: computing multiplicity matrices for admissible representations.

In this project, students will look at the subspaces preserved by matrices. This has applications in linear algebra, control theory and statistical inference and is also theoretically significant.

Topological Data Analysis (TDA) applies classical methods of algebraic topology to investigate and make inferences about the topology of (possibly large/complex) data sets. In this project, students will learn the fundamentals of topological data analysis and apply them to areas of current interest at the interface of geometry, topology and physics.