The augmented marking complex of a surface

We build an augmentation of the Masur-Minsky marking complex by Groves-Manning combinatorial horoballs to obtain a graph we call the augmented marking complex, $\mathcal{AM}(S)$. Adapting work of Masur-Minsky, we prove that $\mathcal{AM}(S)$ is quasiisometric to Teichm\"uller space with the Teichm\"uller metric. A similar construction was independently discovered by Eskin-Masur-Rafi. We also completely integrate the Masur-Minsky hierarchy machinery to $\mathcal{AM}(S)$ to build flexible families of uniform quasigeodesics in Teichm\"uller space. As an application, we give a new proof of Rafi's distance formula for the Teichm\"uller metric.Comment: 30 pages; significantly rewritten to strengthen main construction

Who’s Afraid of the Federal Circuit?

In this brief Essay, Professor Rai responds to Professor Jonathan Masur\u27s Yale Law Journal article Patent Inflation. Professor Masur\u27s argument rests on the assumption that U.S. Patent and Trademark Office ( PTO ) behavior is determined almost entirely by a desire to avoid reversal by the Federal Circuit. Although the PTO is certainly a weak agency over which the Federal Circuit has considerable power, Masur overestimates the extent to which high-level PTO administrators are concerned about Federal Circuit reversals and underestimates institutional influences that are likely to operate in a deflationary direction. The PTO is influenced not only by the Federal Circuit but also by executive branch actors, industry players, and workload concerns that can push in a deflationary direction

Convergence of some horocyclic deformations to the Gardiner-Masur boundary

We introduce a deformation of Riemann surfaces and we are interested in the convergence of this deformation to a point of the Gardiner-masur boundary of Teichmueller space. This deformation, which we call the horocyclic deformation, is directed by a projective measured foliation and belongs to a certain horocycle in a Teichmueller disc. Using works of Marden and Masur and works of Miyachi, we show that the horocyclic deformation converges if its direction is given by a simple closed curve or a uniquely ergodic measured foliation