George H. Brooks

I am a PhD candidate in my fifth year at the University of South Carolina under the advisement of Dr. Linyuan Lu.

My research broadly falls under the area of extremal combinatorics. In essence, for a given type of combinatorial object and a property that objects of this type possess, the primary question is: which object (or objects) maximizes (or minimizes) this property? I explore these kinds of questions in the setting of (hyper)graphs. The properties I have studied include linear combinations of eigenvalues over families of graphs, the ℓ₂-norm of (hyper)graphs, and the order of graphs with positive Lin-Lu-Yau curvature.