Torsion homology of arithmetic lattices and K2 of imaginary fields

We study upper bounds for the torsion in homology of nonuniform arithmetic lattices. Together with recent results of Calegari-Venkatesh, this can be used to obtain upper bounds on K2 of the ring of integers of totally imaginary fields.Comment: Version 2 is a major update. Result for S-integers added. This allows to show case d=2 (imaginary quadratic fields) and d=4 in Theorem 1.3, previously excluded. 12 pages (previously 6

Even unimodular Lorentzian lattices and hyperbolic volume

We compute the hyperbolic covolume of the automorphism group of each even unimodular Lorentzian lattice. The result is obtained as a consequence of a previous work with Belolipetsky, which uses Prasad's volume to compute the volumes of the smallest hyperbolic arithmetic orbifolds.Comment: minor modifications. To appear in J. Reine Angew. Mat

Superconformal interpretation of BPS states in AdS geometries

We carry out a general analysis of the representations of the superconformal algebras SU(2,2/N), OSp(8/4,R) and OSp(8^*/4) and give their realization in superspace. We present a construction of their UIR's by multiplication of the different types of massless superfields ("supersingletons"). Particular attention is paid to the so-called "short multiplets". Representations undergoing shortening have "protected dimension" and correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.Comment: The sections on 6 and 3 dimensions considerably extended; important new references added; misprints correcte

Composite operators and form factors in N=4 SYM

We construct the most general composite operators of N = 4 SYM in Lorentz harmonic chiral ($\approx$ twistor) superspace. The operators are built from the SYM supercurvature which is nonpolynomial in the chiral gauge prepotentials. We reconstruct the full nonchiral dependence of the supercurvature. We compute all tree-level MHV form factors via the LSZ redcution procedure with on-shell states made of the same supercurvature.Comment: 32 page

US open access life cycle

Based on the UK open access life cycle, in the centre circle, we have used the 7 stages of the publishing process as described by Neil Jacobs (Jisc), this is followed by institutional processes – of course not all institutions will have all of these processes up and running, e.g. we don’t all have a CRIS. We then included publisher services that directly impact upon the work of the open access team. We then went on to map above campus services to the life cycle. Finally, we added the 6 sections of OAWAL showing where we think that fits with the life cycle

The Definition and Computation of a Metric on Plane Curves. The Meaning of a Face on a Geometric Model

Two topics in topology, the comparison of plane curves and faces on geometric models, are discussed. With regard to the first problem, a curve is defined to be a locus of points without any underlying parameterization. A metric on a class of plane curves is defined, a finite computation of this metric is given for the case of piecewise linear curves, and it is shown how to approximate curves that have bounded curvature by piecewise linear curves. In this way a bound on the distance between two curves can be computed. With regard to the second problem, the questions to be discussed are under what circumstances do geometrical faces make sense; how can they be explicity defined; and when are these geometrical faces homeomorphic to the realization of the abstract (topological) face

Proofs of the fundamental theorem of algebra

Thesis (M.A.)--Boston University, 1929. This item was digitized by the Internet Archive