5 papers
Generalized Eckardt points on del Pezzo surfaces of degree 1
Julie Desjardins, Yu Fu, Kelly Isham +1
We study intersections of exceptional curves on del Pezzo surfaces of degree 1, motivated by questions in arithmetic geometry. Outside characteristics 2 and 3, at most 10 exception…
Configurations of 10 points and their incidence varieties
Kelly Isham, Nathan Kaplan, Sam Kimport +3
Incidence varieties are spaces of -tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varietie…
Edge-Disjoint Spanning Trees on Star-Product Networks
Kelly Isham, Laura Monroe, Kartik Lakhotia +3
A star-product operation may be used to create large graphs from smaller factor graphs. Network topologies based on star-products demonstrate several advantages including low-diame…
Most subrings of have large corank
Gautam Chinta, Kelly Isham, Nathan Kaplan
If is a sublattice of index , then is a finite abelian group of order and rank at most . Several authors have studied statist…
PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks
Kartik Lakhotia, Laura Monroe, Kelly Isham +4
We present PolarStar, a novel family of diameter-3 network topologies derived from the star product of low-diameter factor graphs. PolarStar gives the largest known diameter-3 netw…