Intro

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Research

My interdisciplinary research develops theory and models to understand the mathematical properties and structure of complex systems.

I am particularly interested in interdisciplinary questions regarding biological processes expressing both continuous and network features. My research praxis fuses applied and computational algebraic topology, mathematical modeling, data science and interdisciplinary collaboration to target challenging problems from epilepsy and neurodegenerative disease to climate change and biodiversity.

I am also interested in geometric and topological representation learning. Below is a list of published and in progress papers.

Publications

• Travis B. Thompson, Bradley Z. Vigil Robert S. Young. Alzheimer's disease and the mathematical mind. Brain Multiphysics, 2024
• pdf
• Bradley Vigil, Robert Young, Travis Thompson. The nerve and graph propagation complexes. (In Preparation) code available on GitHub soon
• pdf
• Bradley Vigil, Robert Young, Travis Thompson. Topological data analysis is a choice (function). (In Preparation).
• pdf
• Robert Young, Naresh Sah, Bradley Vigil, Komoraiah Palle, Sharilyn Almodovar, Yifan Wang, Amanda Laubmeier and Travis Thompson. Decoding Cancer's Defenses: Employing data-driven mathematical modeling to decipher cancer resistance. (In Preparation) code available on GitHub soon
• pdf
• Travis B. Thompson, Boris Decourt, J. Josh Lawrence, Amanda Laubmeier, Yifan Wang, Bradley Vigil, Robert Young, Eleni Keith, Irkan Khan, Andrew Shin, Vijay Hegde, and Naima Moustaid-Moussa. Mouth to Mind: Diet, obesity and mathematical opportunity in Alzheimer's disease research. (In Preparation).
• pdf

Biography

Hello, and welcome! My name is Bradley; I'm a Quad Fellow and Ph.D. candidate in mathematics at Texas Tech University supervised by Dr. Travis Thompson. My research interests focus on Applied Algebraic Topology, Homotopy Theory, and Topological Data Analysis. I am currently interested in problems at the intersection of Applied Algebraic Topology and biological processes on complex networks as well as neuropathologies such as Alzheimer's disease. Furthermore, I have a keen interest in machine learning, in particular, I am interested in the applications and theory of Geometric and Topological Deep Learning.

To learn more about my research, please refer to the research section. You can also download my CV below to learn more about me!

• CV

Talks and Workshops

Talks

Workskops

Contact

• Twitter
• Email
• GitHub

Elements

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