A rigidity result for normalized subfactors

An Interlacing Result on Normalized Laplacians

Strong Singularity for Subfactors

We examine the notion of α-strong singularity for subfactors of a II1 factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its unitary conjugate. Through planar algebra techniques, we demonstrate the existence of a finite index singular subfactor of the hyperfinite II1 factor that cannot be st...

L-betti Numbers for Subfactors

We study L-Betti numbers for von Neumann algebras, as defined by D. Shlyakhtenko and A. Connes in [1], in the presence of a bi-finite correspondence and proof a proportionality formula.

A rigidity result for global Mumford-Shah minimizers in dimension three

We study global Mumford-Shah minimizers in R , introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of u when the singular set K is contained in a smooth enough cone. We then use this monotonicity to prove that for any reduced global minimizer (u,K) in R, if K is contained in a half-plane and touching its edge, then it is the half...

A generalization of Villarreal's result for unmixed tripartite graphs

‎In this paper we give a characterization of unmixed tripartite‎ ‎graphs under certain conditions which is a generalization of a‎ ‎result of Villarreal on bipartite graphs‎. ‎For bipartite graphs two‎ ‎different characterizations were given by Ravindra and Villarreal‎. ‎We show that these two characterizations imply each other‎.