Jonathon Villareal
Jonathon Villareal
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I recently graduated from the University of Louisiana at Lafayette with my Ph.D. in May 2025 studying abstract algebra under Dr. Justin Lynd. My research focuses on fusion systems in finite group theory, particularly, their automorphisms and geometric properties. Fusion systems are finite categories that encode the conjugacy structure of finite groups and their associated centric linking systems. My dissertation relates the automorphisms of fusion systems with their associated centric linking systems at the prime 2 for the finite groups of Lie type. I have also used discrete Morse theory to show that the orbit space of a saturated fusion system is contractible and I am also interested in working with fusion systems from a categorical point of view.
Curriculum Vitae (last Updated: 06/2025)
Degrees
B.S. May 2019 Northwestern State University
Ph.D. May 2025 University of Louisiana at Lafayette
Thesis
Rigid automorphisms of centric linking systems of groups of Lie type (pdf coming)
Ph.D Thesis, University of Louisiana at Lafayette, 2025.
Instructor in Mathematics
Louisiana School (LSMSA)
jvillareal@lsmsa.edu
Articles
[Vil25] Jonathon Villareal. Rigid automorphisms of linking systems of finite groups of Lie type. 2025. arXiv: 2509.21139 [math.GR]. url: https://arxiv.org/abs/2509.21139
[DV25] Dennaoui, Omar and Villareal, Jonathon. Contractibility of the orbit space of a saturated fusion system after Steinberg. Journal of Algebra, 677:267 - 277, 2025.
Travel (Talks Given)
Groups, representations and applications: new perspectives,
Newton Institute, Cambridge, Summer 2022
South Central Topology Conference III
New Mexico State, Las Cruces, New Mexico, Fall 2023
Local AMS Chapter Meeting, ULL, Fall 2023
The contractibility of the orbit space of a saturated fusion system after Steinberg
China-US Group Theory Summit
Florida State, Gainesville, Florida, Spring 2024
The contractibility of the orbit space of a saturated fusion system after Steinberg
Lloyd Roeling Mathematics Conference
University of Louisiana at Lafayette, Lafayette, Louisiana, Spring 2024
The contractibility of the orbit space of a saturated fusion system after Steinberg
Zassenhaus Groups and Friends Conference
Texas State University, San Marcos, Texas, Spring 2024
Rigid automorphisms of centric linking systems of groups of Lie type
Local AMS Chapter Meeting, ULL, Spring 2025
Rigid automorphisms of centric linking systems of groups of Lie type
South Central Topology Conference IV
Texas A&M University, College Station, Texas, Spring 2025
Southern Regional Algebra Conference
University of Louisiana at Lafayette, Lafayette, Louisiana, Spring 2025
Rigid automorphisms of centric linking systems of groups of Lie type
Past Teaching (At LSMSA)
Math 120A: College Algebra (Fall 2025)
Math 303: Calculus I (Fall 2025
Past Teaching (At ULL
Math 103/104: Applied College Algebra Fundamentals (Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2023)
Math 105: Applied College Algebra (Fall 2022)
Math 117: Number Sense for Pk-8 Teachers (Fall 2022, Spring 2023)
Math 250: Survey of Calculus (Spring 2024)
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