Wilson surfaces and higher dimensional knot invariants

An observable for nonabelian, higher-dimensional forms is introduced, its properties are discussed and its expectation value in BF theory is described. This is shown to produce potential and genuine invariants of higher-dimensional knots.Comment: 31 pages, 9 figure

On the isomorphism between the reduction algebra and the invariant differential operators on Lie groups

Using techniques of deformation (bi)quantization we establish a non-canonical algebra isomorphism between the deformed reduction algebra and the invariant differential operators on G/H. Further results concerning other deformations of these two algebras are also proved. Part of the author's PhD thesis at University Paris 7, 2009.Comment: 27 page

Conditional probability estimation

This paper studies in particular an aspect of the estimation of conditional probability distributions by maximum likelihood that seems to have been overlooked in the literature on Bayesian networks: The information conveyed by the conditioning event should be included in the likelihood function as well

The Degree of the Tangent and Secant Variety to a Projective Surface

In this paper we present a way of computing the degree of the secant (resp., tangent) variety of a smooth projective surface, under the assumption that the divisor giving the embedding in the projective space is $3$-very ample. This method exploits the link between these varieties and the Hilbert scheme $0$-dimensional subschemes of length $2$ of the surface.Comment: 20 pages; generalization of the previous version (from projective K3 surfaces to any projective surface) and improvement of the expositio

Empirical interpretation of imprecise probabilities

This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise probabilities can be satisfactorily estimated from data. In fact, estimability on the basis of finite amounts of data is a necessary condition for imprecise probabilities in order to have a clear empirical meaning. Unfortunately, imprecise probabilities can be estimated arbitrarily well from data only in very limited settings

Deformation Quantization and Reduction

This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and pre-Poisson submanifolds, their appearance as branes of the PSM, quantization in terms of L-infinity and A-infinity algebras, and bimodule structures are recalled. As an application, an "almost" functorial quantization of Poisson maps is presented if no anomalies occur. This leads in principle to a novel approach for the quantization of Poisson-Lie groups.Comment: 23 pages, 3 figures; added references, corrected typo