Research & Talks

PhD Research

My PhD research is centered around the global well-possedness and asymptotic behavior of reaction-diffusion equations on network structures describing thin waveguides in various models of mathematical biology (e.g., cardio-vascular systems, thin water channels, dermal tissues) and physics (e.g., graphene, crystals).

Publications 

• Stability and bifurcation for logistic Keller--Segel models on compact graphs (with Wenxian Shen and Selim Sukhtaiev)  Pure and Applied Functional Analysis, 9 (5), 2024, (arXiv -PDF)

• Well-posedness of Keller-Segel systems on compact metric graphs (with Wenxian Shen and Selim Sukhtaiev), Journal of Evolution Equations, 25 (7), 2025,  (Arxiv - PDF) 

• Enhancing Electrocardiography Data Classification Confidence: A Robust Gaussian Process Approach (MuyGPs) ( with U Nnyaba, D Collins, AL Muyskens, B Priest, N Billor) (arXiv - PDF ) 

Talks 

Worcester Polytechnic Institute, Applied Math Seminar  (September 26, 2024)

• Invited talk: Global existence and asymptotic behavior of chemotaxis models on a compact metric graph

AMS Fall Central Sectional Meeting, UT San Antonio, (September 14-15, 202)

• Invited talk in Special Session on Recent trends in differential equations applied to biological processes 

AL-FL JAF DEDS Conference, Florida State University, (May 18-19, 2024)

• Invited talk: Global existence and asymptotic behavior of Chemotaxis models on a compact metric graph

Texas Analysis and Mathematical Physics Symposium, Texas A&M University, (February 9-11, 2024)

• Talk: Chemotaxis models and Keller–Segel systems on compact metric graphs

Analysis and Stochastic Analysis Seminar, Auburn University, (January 31, 2024)

• Talk: Chemotaxis models and Keller-Segel systems on compact metric graphs

SIAM Texas-Louisiana Sectional Meeting (Nov 3-5, 2023)

• Contributed talk: A Chemotaxis Model With A Logistic Source On a Compact Graph

Graduate Student Research Forum (Oct 20, 2023)

• Talk: Guided By Signals: The Mathematics of Chemotaxis

DMS Graduate Student Seminar (Oct 18, 2023)

• Talk: A Chemotaxis Model On a Compact Graph

Posters

KUMUNU-ISU PDE, Dynamical Systems and Applications 2024, University of Kansas, (April 6-7, 2024)

• Poster: Global existence and asymptotic behavior of chemotaxis models on a compact metric graph

Joint Alabama-Florida Conference on Differential Equations, Dynamical Systems and Applications (May 2023)

• Poster: Chemotaxis Models on Compact Graph

Selected Workshops

26th Internet Seminar ”Graphs and Discrete Dirichlet Spaces” (Oct 2022- Feb 2022)

• Followed weekly online lectures and solved exercises with attendees from Auburn University

Graduate Student Mathematical Modeling Workshop (Jun 2021)

• Engaged in a week-long research on Ecological Modeling of Host-Parasitoid Population Dynamics, University of Delaware

• Our final report - Ecological Modeling of host-parasitoid population dynamics