5 papers
The Birthday Paradox for non-backtracking walks on regular graphs
Benjamin Dozier
We show a birthday paradox for random non-backtracking walk on regular graphs of degree at least : such a walk of length has high probability of self-intersecting when i…
Unbounded bunching of saddle connections on the golden L
Benjamin Dozier
We show there is a translation surface (the golden L) that has unbounded bunching: for every positive integer K there exists a ball B of radius 1 in R^2 that contains at least K ve…
Ends of the strata of differentials
Benjamin Dozier, Samuel Grushevsky, Myeongjae Lee
We enumerate the ends of each stratum of meromorphic 1-forms on Riemann surfaces with prescribed multiplicities of zeroes and poles. Our proof uses degeneration techniques based on…
The boundary of a totally geodesic subvariety of moduli space
Frederik Benirschke, Benjamin Dozier, John Rached
We consider subvarieties of , the moduli space of genus Riemann surfaces with marked points, that are totally geodesic with respect to the Teichmülle…
Compactifications of strata of differentials
Benjamin Dozier
In this informal expository note, we quickly introduce and survey compactifications of strata of holomorphic 1-forms on Riemann surfaces, i.e. spaces of translation surfaces. In th…