Current Projects: 2024-2025

Project 1: Ensemble Kalman Filtering

Description: This project will explore the Ensemble Kalman Filter (EnKF) and applications of it. The primary objective is to learn Ensemble Kalman Filter (EnKF) algorithm for solving PDEs with an intent to apply to Fluid Dynamics Problems. The secondary goal is to code the EnKF algorithm in Python or MATLAB.

Mentees: TBD

Mentor: Jonathan Valyou

Project 2: Option Pricing with Monte Carlo

Description: In this project we will study valuing an option using the Black-Scholes Model and discuss Monte Carlo which will be used to derived compare exact and approximate results for comparison.

Mentees: TBD

Mentor: Pervez Ali

Project 3: Comparative study of predictive models in Machine Learning

Description: In this project, we want to investigate the comparative performances of different machine learning techniques such as least squares, stochastic gradient descent, and the Bayesian approach for linear and logistic regression.

Mentees: TBD

Mentor: Rafiq Islam

Project 4: Fundamental Theorem of Algebra

Description: This project includes different proofs of the FTA in different areas like complex analysis, algebraic topology, and there is intuitional geometric interpretation. The most interesting one is the one related to algebraic topology (by using winding numbers). Firstly, we'll focus on fundamental group, and then winding numbers.

Mentee: TBD

Mentor: Ferhat Karabatman

Project 5: Exploring Biomath Modelling Methods

Description: The undergraduate student and mentor will work through one of two modelling techniques (optimal control or agent-based modelling). They may apply it to an already published paper to replicate results or apply it to data from another resource.

Mentee: TBD

Mentor: Dayton Syme

Project 6: Role Extraction for Analyzing Networks

Description: Networks serve as powerful models for representing real-world systems, such as biological networks where genes, proteins, or neurons interact. In these networks, role extraction involves identifying and categorizing nodes based on their structural positions and functional roles. This can be approached through optimization techniques on Riemannian manifolds. Depending on the student’s background and interests, we can explore applications like signed networks or more applied areas like image segmentation, or delve deeper into the theoretical side, like understanding role extraction via Riemannian optimization.

Mentee: TBD

Mentor: Yue Shen

Project 7: Classification of Fake Accounts

Description: We want to work on classification problems, using classic machine learning techniques, if there is interest, we will expand the techniques to deep learning. Classification can be any range of finding fake news, account, or even videos.

Mentee: TBD

Mentor: Navid Bahadoran

Project 8: Modeling Biomath Data and Exploring Parameterization Techniques

Description: Student will assist with modeling tumor data or will either build an agent-based model or learn about optimal control for parameterization.

Mentee: TBD

Mentor: Dayton Syme