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The n-extended affine Lie algebras constitute a class that includes finite dimensional simple Lie algebras (n = 0), irreducible affine Lie algebras (n = 1), and toroidal Lie algebras. For n = 2, closely related Lie algebras appeared in work of Saito and Slodowy in the context of deformation theory of simple elliptic singularities, and in full generality in work of Høegh-Krohn and Torrésani in the context of quantum gauge theory.
Recent results also hint at a new and promising connection between double affine Hecke algebras and Lie superalgebras. Lie superalgebras were initially introduced by physicists in connection with supersymmetry, but the pioneering works of Bernstein, Berezin, Leites and Manin, among others, created a mathematical theory of these algebras. On the other hand, double affine Hecke algebras and their associated Macdonald polynomials can be regarded as a far reaching generalization of the theory of invariant differential operators and spherical polynomials to symmetric spaces. These invariant differential operators, or more precisely their radial parts, admit natural deformations, which also arise in mathematical physics as the completely integrable Calogero–Moser–Sutherland (CMS) systems. The analogous problems for Lie superalgebras and symmetric superspaces have only recently begun to be explored, however there is already a substantial and growing literature on the subject.
One trend in many of these new scenarios in coding theory is the need for algorithmic solutions. For many problems in coding theory, it is possible to come up with nearly optimal solutions (information-theoretically speaking) which are likely very hard for Alice and Bob to actually implement. The goal of algorithmic coding theory is to design solutions which are not only combinatorially good, but are also computationally efficient.
The goal of this workshop is to bring together researchers from several different communities -- applied math, theoretical computer science, communications and electrical engineering -- to focus on a few quickly-moving topics in algorithmic coding theory.
The conference will cover, but is not limited to, the main themes: Algebra, Geometry, dynamical symmetries and conservation laws, mathematical physics and applications.
This in particular includes the themes: Deformation theory and quantization, Hom-algebras and n-ary algebraic structures, Hopf algebra, integrable systems and related mathematical structures, jet theory and Weil bundles, Lie theory and applications, noncommutative geometry, Lie algebras, and more.
The conference will focus on the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and noncommutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, noncommutative dynamics, non-commutative geometry and applications in physics and beyond.
We shall deal with applications to mathematical analysis, like the replacing of Hodges theorem with actual integration of the differential system that specifies Kaehlers exterior and interior derivatives (read curl and divergence). We shall also deal with an additional generalization to Clifford valued differential forms. It takes us beyond Dirac type environments into one that seems appropriate for high energy physics and QM foundations. See arXiv under Jose G Vargas
The goals of the conference are twofold: on the one hand, to inspire the communication of state-of-the-art research within these flourishing areas and the exchange of ideas between them. On the other hand, to give African postgraduates and researchers the opportunity to get in touch with international experts in order to help them enter one of these fields.
Some funding is available to cover travel and local costs of participants.
Last updated: 01 May 2016