For any digraph D let the m-step competition graph C(D) be the graph with the same vertices as D where x and y share an edge in C(D) if in D there are m-step paths from x and y to a common vertex z.… (More)

M. Aguilar Benitez, J. Alcaraz, L. Arruda, F. Barao, A. Barrau, G. Barreira, E. Belmont , J. Berdugo, M. Brinet, M. Buenerd, D. Casadei , J. Casaus , E. Cortina, C. Delgado, C. Diaz, L. Derome, L.… (More)

Operads (or at least An and En operads, which is what we’ll focus on) are a formalism for discussing various degrees to which associativity and commutativity can fail. Suppose I have a space X with a… (More)

Primordial Black Holes (PBHs) are gravitationally collapsed objects that may have been created by density fluctuations in the early universe and could have arbitrarily small masses down to the Planck… (More)

Largely due to the influence of Mike Hopkins and collaborators, stable homotopy theory has become closely tied to moduli theory in algebraic geometry. The benefit of this approach is that all of the… (More)

We report on the performance of the (alpha magnetic spectrometer) AMS Cerenkov counter prototype under a beam of light ions at CERN SPS. In particular the efficiency to determine the velocity and the… (More)

Acknowledgements I would like to thank my advisor, Prof. Michael Hopkins, for introducing me to the beautiful world of stable homotopy theory. I am grateful for the wisdom he shared, and for the time… (More)