We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. Weâ€¦ (More)

Let L âŠ‚ S3 denote an alternating link and Î£(L) its branched double-cover. We give a short proof of the fact that the fundamental group of Î£(L) admits a left-ordering iff L is an unlink. This resultâ€¦ (More)

We study the chromatic number of the curve graph of a surface. We show that the chromatic number grows like k log k for the graph of separating curves on a surface of Euler characteristic âˆ’k. We alsoâ€¦ (More)

Given a one-dimensional homology class in a lens space, a question related to the Berge conjecture on lens space surgeries is to determine all knots realizing the minimal rational genus of all knotsâ€¦ (More)

We employ in situ high-temperature (1030â€“1250 K) scanning tunneling microscopy to measure adatom island coarsening/decay kinetics and temporal fluctuations around the equilibrium shapes ofâ€¦ (More)