Recent Advances in Operator Theory and Operator Algebras

Operator theory and Schubert calculus. Three questions in operator theory. Schubert calculus. The Littlewood-Richardson rule. Practical intersection theory. Back to operators. Bibliography. Non-Self adjoint Operator Algebras: dynamics, classi_cation and C_-envelopes. Introduction. Examples. C*correspondences. Adding tails to a C_-correspondence. The C_-envelope of an operator algebra. Dynamics and classi_cation of operator algebras. Crossed products of operator algebras. Local maps and representation theory. Bibliography. An introduction to Sofic entropy. Introduction. Internal and external approximation. Amenable measure entropy. Amenable topological entropy. Sofic measure entropy. Sofic topological entropy. Dualizing Sofic measure entropy. Algebraic actions. Further developments. Bibliography. The solution of the Kadison-Singer Problem: yet another presentation. Introduction. The Kadison-Singer problem. Intermezzo: what we will do next and why. Analytic functions and univariate polynomials. Several variables: real stable polynomials. Characteristic and mixed characteristic polynomials. Randomisation. Proof of the Paving Conjecture. Final Remarks. Bibliography.