Talks

The theory of statistical comparison was formulated (chiefly by David Blackwell in the 1950s) in order to extend the theory of majorization to objects beyond probability distributions, like multivariate statistical models and stochastic transitions, and has played an important role in mathematical statistics ever since. The central concept in statistical comparison is the so-called "information ordering," according to which information need not always be a totally ordered quantity, but often takes on a multi-faceted form whose content may vary depending on its use. In this talk, after reviewing the basic ideas of statistical comparison with an emphasis on their operational character, I will discuss various generalizations to quantum theory (and beyond). I will then argue that quantum statistical comparison provides a natural framework, somehow complementary to semi-definite programming, to study quantum resource theories, with explicit examples given by the resource theories of quantum nonlocality, quantum communication, and quantum thermodynamics.

Using knowledge about the spectrum of operators in N=4 SYM, consistency of OPE, and analytic bootstrap techniques, I will obtain 1- loop corrections for 4-pt functions of single particle half-BPS operators of IIB supergravity on AdS_5\timesS^5. Along the way, I will discuss a general formula for the leading anomalous dimension of all double-trace operators in the supergravity regime.

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks. 

The goal of this series is to collect various different formulations of General Relativity, with emphasis on four spacetime dimensions and formulations that use differential forms. The (non-exhaustive) list of formulations to be covered is per this plan:

Lecture 1): Motivations, followed by the usual Einstein-Hilbert to start with, first order Palatini, second order pure affine connection Eddington-Schroedinger.

Lecture 2) Cartan's geometry of soldering. First order Einstein-Cartan tetrad formulation, second order pure spin connection formulation, MacDowell-Mansouri formulation.

Lecture 3) Non-chiral BF-type formulations. Explicit pure spin connection Lagrangian, field redefinitions, BF plus potential for the 2-form field formulation.

Lecture 4) Chiral formulations in four dimensions. Chiral Einstein-Cartan, Plebanski formulation, pure SU(2) connection formulation, SU(2) BF plus potential for the 2-form field. Self-dual gravity. Concluding remarks.