2025 - Research Experience for Undergraduates

Summer School on Mathematical Foundation of Data Science

June 2, 2025 – July 11, 2025
LeConte 101
Department of Mathematics
University of South Carolina

Or join the virtual Zoom program:
Join the Zoom meeting
Meeting ID: 894 6318 3663
Passcode: 024115

Sponsored by:
Department of Mathematics, University of South Carolina
National Science Foundation RTG award DMS 2038080

Organized by:
Prof. Linyuan Lu, Prof. Qi Wang, Prof. Peter Binev, Prof. Pooyan Jamshidi, Prof. Ray Bai, Prof. Changhui Tan, Prof. Siming He

Program Overview

This REU summer program is part of the NSF RTG project RTG: Mathematical Foundation of Data Science at University of South Carolina, which aims to develop a multi-tier research training program at the University of South Carolina designed to prepare the future workforce in a multidisciplinary paradigm of modern data science.

The education and training model leverages existing faculty expertise and brings in new talent to foster mathematical data science research and training through vertical integration of postdoctoral researchers, graduate students, undergraduate students, and advanced high school students.

A primary focus of this project is to recruit and train U.S. citizens, women, and underrepresented minority students and postdoctoral researchers through research-led training in data science.

For more information on the NSF RTG project, visit the Mathematical Foundation of Data Science RTG page.

Starting from the first week, students will be divided into several groups to work on research projects. Guest speakers will also give talks on the latest developments in the mathematical foundation of data science. On the last day of the program, students will present their research findings.

Research Projects

Developing AI Tools for Scanning Tunneling Microscopy (STM)

Advisor: Peter Binev

Scanning Tunneling Microscopy (STM) is used to observe the atomic structure of material surfaces. Data acquisition tasks in STM usually require a human-in-the-loop component to constantly evaluate structural phenomena on the surface and navigate toward areas of interest. Using AI to handle most of these evaluations could significantly accelerate materials research.

This project involves developing data-processing tools and deep learning routines to recognize common structures and classify them. Students will investigate and train deep learning autoencoders to extract pattern information from artificial and real data and use that information to support image-processing tasks.

Further information about the research area can be found in last year’s project report.

AI Tools for Digital Twins for Health

Advisor: Qi Wang

Biomedical applications are ideal implementation venues for AI models and tools. With AI integration, biomedical research and healthcare delivery could experience transformational change.

The goal of this project is to develop biomedical AI models, data-processing methods, and computational infrastructure to support AI-enabled digital twins for health. The REU component will include adding front-end user interfaces for basic disease models so they can be used in clinical settings.

The three major tasks in the current digital twin project include data imputation and synthetic data generation, multiclass classification, and time-series forecasting. Students will work with an existing research group to implement developed models and modules, with opportunities to extend the platform further.

From Language to Action: Distributed LLM-Based Robot Control and Planning

Advisors: Pooyan Jamshidi and Abir Hossen

This project explores the synergy between large language models and robotics, especially task planning and execution through:

• Translating natural language commands into robot actions
• Multi-modal task planning using visual and textual information

Students will explore a distributed LLM strategy and work toward a framework that demonstrates robotic movement, object manipulation, and combined tasks based on natural language commands.

The project will primarily involve building unified software and may use technologies such as Ollama, Cake, ROS, Python, and Flask APIs. The goal is to make the framework software- and hardware-agnostic.

Spatiotemporal Modeling for Disease Mapping and Causal Inference

Advisor: Ray Bai

Disease mapping is a critical public health task that analyzes the distribution and spread of disease across time and space. Bayesian spatiotemporal modeling is widely used to predict disease prevalence and identify county-level characteristics associated with disease trends.

In this project, students will use Bayesian spatiotemporal models to predict disease prevalence at the county level in the United States. If time allows, the project will also extend into causal inference to examine whether specific county-level characteristics may contribute to changes in disease prevalence.

Simulating Transport and Diffusion in Physical and Biological Systems

Advisors: Changhui Tan and Siming He

This project explores how transport (directed movement) and diffusion (random spreading) interact in systems governed by partial differential equations (PDEs). These models arise in many applications, including biological population spread and material phase separation.

Students will develop MATLAB code to simulate the PDEs numerically. The project includes:

• Learning basic PDE concepts related to transport and diffusion
• Developing numerical schemes to solve the equations
• Running numerical experiments to study how transport changes diffusion-driven behavior

This project is well suited for students interested in scientific computing, numerical modeling, and data-driven approaches to real-world systems.

Ricci Curvature on Graphs

Advisor: Linyuan Lu

Over the last several decades, extensive work has adapted the concept of Ricci curvature from Riemannian geometry to graph-based settings. This allows graphs to be studied in ways similar to manifolds.

Curvature has applications in network analysis, quantum computation, and dynamic networks. In this project, students will explore the characteristics of graphs exhibiting positive Lin-Lu-Yau Ricci curvature.

Program Calendar

Week 1

Week 2

Week 3

Week 4

Week 5

Week 6

Contact Information

Faculty

• Linyuan Lu — lu@math.sc.edu — Profile
• Peter Binev — binev@math.sc.edu — Profile
• Qi Wang — Qwang@math.sc.edu — Profile
• Pooyan Jamshidi — PJAMSHID@cse.sc.edu — Profile
• Ray Bai — RBAI@mailbox.sc.edu — Profile
• Changhui Tan — TAN@math.sc.edu — Profile
• Siming He — SIMING@mailbox.sc.edu — Profile

Postdoctoral Researcher

• William Linz — wlinz@mailbox.sc.edu
• George Brooks — ghbrooks@email.sc.edu

Graduate Assistants

• Teegan Bailey — teeganb@email.sc.edu
• Jasdeep Singh — jasdeep@email.sc.edu
• Sehwan Kim — sehwank@email.sc.edu
• Henry Simmons — has11@email.sc.edu
• Nizam Hasanov — nhasanov@email.sc.edu

Undergraduate Students

• Aidan Van Voorhis — vanvoora@email.sc.edu — University of South Carolina — In-Person
• Angelina Piccolino — piccola@email.sc.edu — University of South Carolina — Virtually
• Aydyn Rohm — arohm@email.sc.edu — University of South Carolina — In-Person
• Evan Funderburg — ewf@email.sc.edu — University of South Carolina — Virtually
• Ibrahim Hussain — i.hussain2304@gmail.com — Boston University — In-Person
• Lea Frost — lkfrost@email.sc.edu — University of South Carolina — Virtually
• Mark Ritchie — RITCHIED@email.sc.edu — University of South Carolina — In-Person
• Nathanael Johnson — nathan.erikson.9701@gmail.com — The Ohio State University — In-Person
• Niyathi Kukkapalli — nk6074@princeton.edu — Princeton University — Virtually
• Nolan Jones — jonesnt@email.sc.edu — University of South Carolina — In-Person
• Ronald Smith — Ronaldrs@email.sc.edu — University of South Carolina — Virtually
• Sai Kottapali — kottapas@email.sc.edu — University of South Carolina — Virtually
• Samatha Criswell — criswes@email.sc.edu — University of South Carolina — In-Person
• Sara Shree Ramadoss Muthuselvam — muthuses@email.sc.edu — University of South Carolina — Virtually
• Shahyad Khamnei — shahyadkhamnei1@gmail.com — Boston University — Virtually
• Wynton Vaughn — wyntonv@g.clemson.edu — Clemson University — In-Person
• Zachary Valsecchi — zvv@email.sc.edu — University of South Carolina — In-Person
• Emmy Sitnik — esitnik@email.sc.edu — University of South Carolina — In-Person