Pure and Applied Mathematics Journal

Special Issue

Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program

  • Submission Deadline: 30 November 2014
  • Status: Submission Closed
  • Lead Guest Editor: Francisco Bulnes
About This Special Issue
Derived categories and their deformed versions are used to develop a theory of the ramifications of field studied in the geometrical Langlands program to obtain the correspondences between moduli stacks and solution classes in field theory, represented cohomologically under several versions of generalized Penrose transforms.
Lead Guest Editor
  • Francisco Bulnes

    Research Department in Mathematics and Engineering, Technological Institute of High Studies of Chalco (TESCHA), Chalco, Mexico

Guest Editors
  • Yuri Stropovsvky

    Baikov Institute of Material Sciencies Research, Moscow, Russian Federation

Published Articles
  • Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes

    Sergei Fominko

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 38-43
    Received: 3 December 2014
    Accepted: 8 December 2014
    Published: 10 January 2015
    DOI: 10.11648/j.pamj.s.2014030602.17
    Abstract: The DX-schemes (and their particular tools example jets) are related to determine conformal blocks of space-time pieces that are invariant under conformal transformations. All algebras will be commutative and Sym will always denote SymOX However, all Hom, and , will be understood over the base field k. This will permit the construction of one forma... Show More
  • Integral Geometry and Complex Space-Time Cohomology in Field Theory

    Francisco Bulnes , Ronin Goborov

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 30-37
    Received: 4 December 2014
    Accepted: 6 December 2014
    Published: 27 December 2014
    DOI: 10.11648/j.pamj.s.2014030602.16
    Abstract: Through of a cohomological theory based in the relations between integrating invariants and their different differential operators classes in the field equations as well as of functions inside of the integral geometry are established equivalences among cycles and co-cycles of the closed sub-manifolds, line bundles and contours of the space-time mod... Show More
  • The Recillas’s Conjecture on Szegö Kernels Associated to Harish-Chandra Modules

    Francisco Bulnes , Kubo Watanabe , Ronin Goborov

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 26-29
    Received: 22 November 2014
    Accepted: 27 November 2014
    Published: 29 November 2014
    DOI: 10.11648/j.pamj.s.2014030602.15
    Abstract: The solution of the field equations that involves non-flat differential operators (curved case) can be obtained as the extensions Φ+Szegö operators in G/K with G, a non-compact Lie group with K, compact. This could be equivalent in the context of the Harish-Chandra modules category to the obtaining of extensions in certain sense (Cousin complexes o... Show More
  • Functors on ∞- Categories and the Yoneda Embedding

    Yuri Stropovsvky

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 20-25
    Received: 12 November 2014
    Accepted: 18 November 2014
    Published: 24 November 2014
    DOI: 10.11648/j.pamj.s.2014030602.14
    Abstract: Through the application of the Yoneda embedding in the context of the ∞- categories is obtained a classification of functors with their corresponding extended functors in the geometrical Langlands program. Also is obtained a functor formula that can be considered in the extending of functors to obtaining of generalized Verma modules. In this isomor... Show More
  • Moduli Spaces, Non-Commutative Geometry and Deformed Differential Categories

    Ivan Verkelov

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 12-19
    Received: 25 October 2014
    Accepted: 2 November 2014
    Published: 5 November 2014
    DOI: 10.11648/j.pamj.s.2014030602.13
    Abstract: The following research plays a central role in deformation theory. If x, is a moduli space over a field k, of characteristic zero, then a formal neighborhood of any point xϵx, is controlled by a differential graded Lie algebra. Then using the derived categories language we give an analogous of the before sentence in the setting of non-commutative g... Show More
  • Coverings and Axions: Topological Characterizing of the Energy Coverings in Space-Time

    Mario Ramírez , Luis Ramírez , Oscar Ramírez , Francisco Bulnes

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 6-11
    Received: 8 October 2014
    Accepted: 11 October 2014
    Published: 24 October 2014
    DOI: 10.11648/j.pamj.s.2014030602.12
    Abstract: Inside the QFT and TFT frame is developed a geometrical and topological model of one wrapping energy particle or “axion” to establish the diffeomorphic relation between space and time through of universal coverings. Then is established a scheme that relates both aspects, time and space through of the different objects that these include and their s... Show More
  • Integral Geometry Methods on Deformed Categories in Field Theory II

    Francisco Bulnes

    Issue: Volume 3, Issue 6-2, December 2014
    Pages: 1-5
    Received: 8 October 2014
    Accepted: 11 October 2014
    Published: 24 October 2014
    DOI: 10.11648/j.pamj.s.2014030602.11
    Abstract: The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations ... Show More