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Mathematics Department Colloquium : Spring 2010 schedule


   Wednesday, March 17, 1530-1630.

SPEAKER : Alexander Stolin, GU/Chalmers.

TITLE : Classification of double Lie algebras

ABSTRACT : Let me first remind you of the definition of dual numbers over the complex numbers: They are numbers of the form a+eb, where a,b are complex numbers and e is a formal number such that the square of e is zero. Clearly, the set fo dual numbers forms a vector space of dimension 2. More generally, we call any algebra of dimension 2 a "double algebra". It is not difficult to prove that, along with the dual numbers, there exists only one other double algebra, namely the algebra of pairs (a,b) with componentwise operations.

It turns out that double Lie algebras can be defined for any Lie algebra in a similar (but, of course, much more complicated) way.

In my talk I will present a classification of double Lie algebras over Lie algebras of the form g[u] and g[[u]], where g is a simple finite dimensional Lie algebra and u is a formal variable (usually referred to in physics as the "spectral parameter"). This is joint work with F. Montaner (Spain) and E. Zelmanov (USA).


   Monday, January 25, 1530-1630.

SPEAKER : Robert Berman, Chalmers/GU.

TITLE : Complex Geometry in Equilibrium

ABSTRACT : In this lecture I will explain how Complex Geometry can be used to solve two seemingly unrelated problems. The first one concerns the question about how to find an optimal distribution of sampling/interpolation nodes for large degree polynomials (with recent applications in the statistical theory of Optimal Experimental Designs). The second problem concerns finding canonical "polynomial" approximations to certain non-linear partial differential equations (with recent applications in string theory). As it turns out both these two problems are in a sense dual formulations of one single problem which concerns "convergence towards equilibrium" on a complex manifold.


   Monday, January 11, 1530-1630.

SPEAKER : Ann-Brith Strömberg, Chalmers/GU.

TITLE : Optimization of maintenance planning - applications, mathematical modelling, characteristics, and challenges

ABSTRACT : In this lecture I give the practical background to a set of mathematical models of optimization problems related to industrial maintenance activities. I describe some important mathematical properties of these combinatorial optimization problems. Then, I describe the computational complexity and numerical solutions methods for these models and show some interesting challenges.