Programma Giovedì 13 Aprile 

Aspetti Geometrici e Topologici


Francesco Bonechi (I.N.F.N., Firenze)The Poisson sigma model and the quantization of Poisson manifoldsAbstract: The Poisson sigma model is a bidimensional field theory having as target manifold a Poisson manifold. Kontsevich formula for the deformation quantization of the target manifold is interpretable as the perturbative expansion of a particular correlator of the model. The non perturbative dynamics of the model is instead still largely unexplored. In this seminar, we clarify the meaning of the inegrality condition of the Poisson tensor which appears both in the integration of the gauge transformations of the model and in the geometric quantization of the target manifold. Francesco D'Andrea (S.I.S.S.A., Trieste)Local index formulas on quantum spheresAbstract: A general introduction to the basic ideas of
index theory in noncommutative geometry is presented, clarified through
the qsphere example. One of the main motivation of this work is the
classification of deformations of instantons, whose charge can be computed
using the local formulae of ConnesMoscovici. After a brief introduction
of the main notions, some results concerning the geometrical properties of
the quantum SU(2) group and of Podles spheres, which are deformation of
the Lie group SU(2) and of Riemann sphere, respectively, will be discussed. Jarah Evslin (Free University, Bruxelles)Twisted KTheory as a BRST CohomologyAbstract: We argue that twisted Ktheory is a BRST cohomology. The original Hilbert space is the integral cohomology of a spatial slice, corresponding to the lattice of quantized RamondRamond field strengths. The gauge symmetry consists of large gauge transformations that correspond geometrically to choices of trivializations of gerbes. The BRST operator is identified with the differential of the AtiyahHirzebruch spectral sequence. Branislav Jurco (Munich University, Munich)Nonabelian gerbes, differential geometry and stringy applicationsAbstract: We will discuss nonabelian gerbes and their twistings as well as the corresponding differential geometry. We describe the classifying space, the corresponding universal gerbe and their relation to string group and string bundles. Finally we show the relevance of twisted nonabelian gebres in the study and resolution of global anomalies of multiple coinciding M5branes. Urs Schreiber (Hamburg University, Hamburg)Surface transport, gerbes, TFT and CFTAbstract: Segal's conception of a 2D QFT as a functor on cobordisms may be refined to that of a 2functor on surface elements. Surface transport in gerbes, as well as 2D TFTs and CFTs provide examples. Alessandro Tanzini (SISSA Trieste)Recent developments in topological brane theoriesAbstract: We will discuss the formulation of topological theories for branes and its relevance for the recent conjectures about Sduality in topological string and topological M theory.
Alessandro Torrielli (Humboldt University, Berlin)Dbrane decay in electric fields and noncommutative geometryAbstract: We study tachyon condensation in the presence of overcritical electric fluxes, by means of a toy model based on the noncommutative deformation of the one proposed by Minahan and Zwiebach. We discuss the relation with Sen's standard picture of Dbrane decay, and the connection with the Sbrane paradigma. Maxim Zabzine (Upsala University, Upsala, and University of California, Santa Barbara)New results in generalized Kahler geometryAbstract: I will review the different decsriptions of generalized Kahler geometry and its relation with N=(2,2) supersymmetric sigma model. I will sketch the proof of the existence of generalized Kahler potential and will explain the relation to offshell supersymmetry. 