Philip Hackney

On the Minimum Rank Among Positive Semidefinite Matrices with a Given Graph

Let

On the minimum semidefinite rank of a simple graph

mathcal{P}(G)

On the Category of Props

be the set of all positive semidefinite matrices whose graph is

Group actions on Segal operads

G

The homotopy theory of simplicial props

, and

Relative left properness of colored operads

operatorname{msr}(G)

Reedy categories which encode the notion of category actions

be the minimum rank of all matrices in

Operations in the homology spectral sequence of a cosimplicial infinite loop space

mathcal{P}(G)

Infinity properads and infinity wheeled properads

. Upper and lower bounds for

Homology operations and cosimplicial iterated loop spaces

operatorname{msr}(G)