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