Contractibility of the orbit space of a saturated fusion system after Steinberg
Mathematics · UL Lafayette
Omar Dennaoui
I study finite groups locally at a prime p, and the higher-categorical structures that encode them: partial groups, fusion systems, Segal conditions, and nerve theorems.
Research
I'm a graduate student advised by Justin Lynd and Philip Hackney. My thesis has two connected threads:
Localities & higher Segal
The higher Segal degree of localities of symmetric and alternating groups at the prime 2.
Nerve theorems
Nerve theorems for higher categorical structures via monads, including cyclic multicategories.
More broadly, I think about fusion systems and their homotopy theory and homological algebra, and modular representation theory.
Articles
Talks
Earlier talks on the orbit space of a fusion system (4)
Teaching
Math 109/109S · Pre-Calculus Algebra
Math 105/105S · Applied College Algebra Fundamentals
Math 105 · Applied College Algebra
Math 103/104 · Applied College Algebra Fundamentals
Education
Ph.D. Mathematics, University of Louisiana at Lafayette
B.S. Mathematics with honors, University of Balamand, Lebanon