Justin Lynd Associate Professor University of Louisiana at Lafayette Maxim Doucet Hall Lafayette, LA 70504 lynd@louisiana.edu Office: Maxim Doucet Hall 408 Curriculum Vitae (last updated: 08/2022)

I am an Associate Professor and Devon Endowed Professor of Mathematics at the University of Louisiana at Lafayette. Before coming to Louisiana, I was a postdoc at the University of Aberdeen, the University of Montana, and Rutgers University. Before that, I was a graduate student at Ohio State, where my advisor was Ron Solomon.

My research is on the structure of finite groups around a prime p, and especially how that structure interacts with adjacent fields. I tend to think most about partial groups, fusion systems and their associated homotopy theory and homological algebra, and modular representation theory.

I am on leave during academic year 2024-2025.

Articles

• Cohomology on the centric orbit category of a fusion system (arXiv), with George Glauberman
  submitted, 11pp.
• Partial groups as symmetric simplicial sets (arXiv), with Philip Hackney
  submitted, 22pp.

1. Realizing finite groups as automizers (doi, arXiv), with Sylvia Bayard
   J. Group Theory (2024)
2. Punctured groups for exotic fusion systems (doi, arXiv), with Ellen Henke and Assaf Libman
   Trans. London Math. Soc. 10 (2023), no. 1, 21-99.
3. Weights in a Benson-Solomon block (doi, arXiv), with Jason Semeraro
   Forum Math. Sigma 11 (2023), Paper No. e60.
4. Fusion systems with Benson-Solomon components (doi, arXiv), with Ellen Henke
   Duke Math. J., 171 (2022), no. 3, 673-737.
5. Rigid automorphisms of linking systems (doi, arXiv), with George Glauberman
   Forum Math. Sigma 9 (2021), Paper No. e23.
6. Centers of Sylow subgroups and automorphisms (doi, arXiv), with George Glauberman, Robert Guralnick, and Gabriel Navarro
   Israel J. Math 240 (2020), no. 1, 253-266.
7. Weight conjectures for fusion systems (doi, arXiv), with Radha Kessar, Markus Linckelmann, and Jason Semeraro
   Adv. Math. 357 (2019), 40pp.
8. Extensions of the Benson-Solomon fusion systems (doi, arXiv), with Ellen Henke
   in Geometric and Topological Aspects of the Representation Theory of Finite Groups,
   Springer Proc. Math. Stat. 242 (2018), 251-268.
9. Fusion systems with some sporadic J-components (doi, arXiv), with Julianne Rainbolt
   J. Algebra 489 (2017), 165-178.
10. Control of fixed points and existence and uniqueness of centric linking systems (doi, arXiv) with George Glauberman
    Invent. Math. 206 (2016), no.2, 441-484.
11. A characterization of the 2-fusion system of L₄(q) (doi, arXiv),
    J. Algebra 428 (2015), 315-356.
12. The Thompson-Lyons transfer lemma for fusion systems (doi, arXiv),
    Bull. Lond. Math. Soc. (2014) 46 (6): 1276-1282
13. Weak closure and Oliver's p-group conjecture (doi, arXiv), with David J. Green.
    Israel J. Math. 197 (2013), no. 1, 497-507.
14. 2-subnormal quadratic offenders and Oliver's p-group conjecture (doi, arXiv)
    Proc. Edin. Math. Soc. 56 (2013), 211-222.
15. Analogues of Goldschmidt's thesis for fusion systems (doi, arXiv), with Sejong Park
    J. Algebra 324 (2010), 3487-3493.

Thesis

• A characterization of the 2-fusion system of L₄(q) (pdf)
  Ph.D. Thesis, The Ohio State University, 2012.

Upcoming Travel

Topology, representation theory, and higher structures, Isle of Skye, May 26-June 22, 2024.
Masterclass: Exit paths and stratified homotopy types, University of Copenhagen, June 24-June 28, 2024.
Joint perspectives in geometry, algebra, and topology, CRM Barcelona, July 1-July 5, 2024.
AMS Western Sectional Meeting, University of California, Riverside, October 26-27, 2024.
Finite groups, fusion systems, and applications, Oberwolfach, March 16-21, 2025.