Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program
View Published Articles →01About 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.02Meet the Guest Editors
Our distinguished editors bring deep subject-matter expertise to curate high-quality research and ensure a rigorous peer-review process.
Lead Guest Editor
Francisco Bulnes
Research Department in Mathematics and Engineering, Technological Institute of High Studies of Chalco (TESCHA), Chalco, Mexico
Guest Editor
Yuri Stropovsvky
Baikov Institute of Material Sciencies Research, Moscow, Russian Federation
03Published Articles
The following articles have been published in this special issue.
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Approaching by DX- Schemes and Jets to Conformal Blocks in Commutative Moduli Schemes
Issue: Volume 3, Issue 6-2, December 2014Pages: 38-43Received: 3 December 2014Accepted: 8 December 2014Published: 10 January 2015Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 30-37Received: 4 December 2014Accepted: 6 December 2014Published: 27 December 2014Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 26-29Received: 22 November 2014Accepted: 27 November 2014Published: 29 November 2014Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 20-25Received: 12 November 2014Accepted: 18 November 2014Published: 24 November 2014Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 12-19Received: 25 October 2014Accepted: 2 November 2014Published: 5 November 2014Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 6-11Received: 8 October 2014Accepted: 11 October 2014Published: 24 October 2014Abstract: 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
Issue: Volume 3, Issue 6-2, December 2014Pages: 1-5Received: 8 October 2014Accepted: 11 October 2014Published: 24 October 2014Abstract: 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
