John Rached

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math.GT2024

The boundary of a totally geodesic subvariety of moduli space

Frederik Benirschke, Benjamin Dozier, John Rached

We consider subvarieties $N$ of $M_{g, n}$ , the moduli space of genus $g$ Riemann surfaces with $n$ marked points, that are totally geodesic with respect to the Teichmülle…

math.GT2022

Counting Closed Geodesics in Rank 1 $SL (2, R)$ -orbit Closures

John Rached

We obtain bounds on the numbers of intersections between triangulations as the conformal structure of a surface varies along a Teichm{ü}ller geodesic contained in an $\mathrm{SL}\l…

The boundary of a totally geodesic subvariety of moduli space

Counting Closed Geodesics in Rank 1 SL(2,R)-orbit Closures

Counting Closed Geodesics in Rank 1 $SL (2, R)$ -orbit Closures