This BIRS workshop stimulated a lot of ideas. To begin with, I was able to make progress on a collaboration with Steven Sivek regarding interactions between contact geometry and the fundamental group. I started new collaborations with Hedden involving 1) a project to use my (with Vela-Vick, Vertesi) BRAID version of the transverse invariant in knot Floer homology to prove that the rank of HFK reduced gives a bound on the fractional Dehn twist coefficients of braid representatives of a given knot. In particular, we believe that rkHFK_red(K,a) bounds the FDTCs of braid representatives of K with sl=2a-1, and 2) a project to compute the Heegaard Floer homology of the union of two manifolds with torus boundaries by computing a cube of resolutions complex where all the higher polygon counting takes place on the torus (and therefore ought to be computable).

[link to this testimonial]

This workshop definitely helped me to continue my research with Baptiste Chantraine on positive contact isotopies. It also revealed me interesting questions around foliation theory and I was able to exchange a lot with Rachel Roberts and Will Kazez on these.

[link to this testimonial]