My research is in free probability, focused in the non-tracial case (i.e. type III von Neumann algebras), and most of my results are concerning the idea of free transport due to Guionnet and Shlyakhtenko. I also have work related to subfactor planar algebras and the emerging field of bi-free probability.

# Publications

**Free monotone transport without a trace**; Comm. Math. Phys.**334**(2015), no. 3, 1245-1298.**Free transport for finite depth subfactor planar algebras**; J. Funct. Anal.**268**(2015), no. 9, 2586–2620.**Combinatorics of bi-freeness with amalgamation**, with I. Charlesworth and P. Skoufranis; Comm. Math. Phys.**338**(2015), no. 2, 801–847.**On two-faced families of non-commutative random variables**, with I. Charlesworth and P. Skoufranis; Canad. J. Math.**67**(2016), no. 6, 1290-1325.**An application of free transport to mixed $q$-Gaussian algebras**, with Q. Zeng; Proc. Amer. Math. Soc.,**144**(2016), no. 10, 4357-4366.**Free montone transport for infinite variables**, with Q. Zeng; Int. Math. Res. Not. IMRN, to appear (2017).**On finite free Fisher information for eigenvectors of a modular operator**; J. Funct. Anal.**273**(2017), no. 7, 2292-2352**Free Stein kernels and an improvement of the free logarithmic Sobolev inequality**, with M. Fathi; Adv. Math.,**317**(2017), no. 7, 193-223.**Free transport for interpolated free group factors**, with M. Hartglass; J. Funct. Anal.**274**(2017), no. 1, 222-251