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Algebraic Lie Theory
By Cambridge University
Algebraic Lie Theory episodes
- 1 hr 3 min
- 1 hr 3 min
- Trying to construct explicitly kernels for Langlands' functoriality 3Lafforgue, L (IHES)Tuesday 19 May 2009, 10:00-12:002 hr 3 min
- 1 hr 4 min
- Cluster algebras via quivers with potentialsZelevinsky, A (Northeastern University)Thursday 14 May 2009, 15:15-16:151 hr
- Refinements of the Bruhat decomposition and structure constants of Hecke algebras of finite Chevally groupsCurtis, CW (Oregon)Thursday 14 May 2009, 14:00-15:0058 min
- Trying to construct explicitly kernels for Langlands' functoriality 2Lafforgue, L (IHES)Tuesday 12 May 2009, 10:00-12:002 hr 22 min
- Quiver presentations of descent algebras of finite Coxeter groupsPfeiffer, G (National University of Ireland)Thursday 07 May 2009, 15:15-16:151 hr 4 min
- Some geometric constructions of link homologyWilliamson, G (Oxford)Thursday 07 May 2009, 14:00-15:0057 min
- Trying to construct explicitly kernels for Langlands' functoriality 1Lafforgue, L (IHES)Tuesday 05 May 2009, 10:00-12:002 hr 16 min
About Algebraic Lie Theory
From the publisher's feed
Lie theory has profound connections to many areas of pure and applied mathematics and mathematical physics. In the 1950s, the original "analytic" theory was extended so that it also makes sense over arbitrary algebraically closed fields, in particular, fields of positive characteristic. Understanding fundamental objects such as Lie algebras, quantum groups, reductive groups over finite or p-adic fields and Hecke algebras of various kinds, as well as their representation theory, are the central themes of "Algebraic Lie Theory".
A driving force has always been the abundance of challenging, yet very basic problems, like finding explicit character formulae for representations. The introduction of geometric methods (in the 1970s) has revolutionized the field. It led to a flow of new ideas between several disciplines, and produced spectacular advances. The ideas of "geometrization" and "categorification" now play a fundamental role in the development of the subject. New structures continue to arise from connections with other areas of mathematics and mathematical physics, like the emerging theory of W-algebras.
Read more at: www.newton.ac.uk/programmes/ALT/