B semileptonic moments at NNLO

The calculation of the moments in inclusive B meson semileptonic decays is upgraded to O(alphas^2). The first three moments of the lepton energy and invariant hadronic mass distributions are computed for arbitrary cuts on the lepton energy and in various renormalization schemes, finding in general small deviations from the O(alphas^2 beta0) calculation. I also review the relation between MSbar and kinetic heavy quark masses.Comment: 28 pages, 9 figure

Precision Electroweak Measurements Circa 2002

Present global fits to electroweak data are characterized by two results that differ from Standard Model expectations by about 3 sigma, the NuTeV measurement of sin^2theta_W and the FB b quark asymmetries measured at LEP. I review possible SM and new physics explanations of these anomalies and the implications for the indirect determination of the Higgs mass.Comment: 6 pages, 2 figures, talk at ICHEP, Amsterdam, 24-31 July 200

Semileptonic and radiative B decays circa 2005

I briefly review the theoretical status of semileptonic and radiative B decays in 2005.Comment: 6 pages, 1 fig, review talk at Beauty 2005, Assisi, June 20-24 200

Normalizing inclusive rare B decays

The inclusive semileptonic branching ratio is often employed to normalize other inclusive B decays. Using recent determinations of the non-perturbative parameters of the Operator Product Expansion we compute the normalization factor for the branching ratio of B->X_s gamma and find a few percent enhancement with respect to previous determinations.Comment: 11 pages, 1 fig; minor numerical changes, text improved, matches version to appear in PL

Towards a constructive simplicial model of Univalent Foundations

We provide a partial solution to the problem of defining a constructive version of Voevodsky's simplicial model of univalent foundations. For this, we prove constructive counterparts of the necessary results of simplicial homotopy theory, building on the constructive version of the Kan-Quillen model structure established by the second-named author. In particular, we show that dependent products along fibrations with cofibrant domains preserve fibrations, establish the weak equivalence extension property for weak equivalences between fibrations with cofibrant domain and define a univalent classifying fibration for small fibrations between bifibrant objects. These results allow us to define a comprehension category supporting identity types, $\Sigma$-types, $\Pi$-types and a univalent universe, leaving only a coherence question to be addressed.Comment: v3: changed the definition of the type Weq(U) of weak equivalences to fix a problem with constructivity. Other Minor changes. 31 page