Alexander Veselov (Loughborough University)
A.P.Veselov@lboro.ac.uk The Huygens Principle in the narrow Hadamard sense means that the fundamental solution of the corresponding hyperbolic equation is located on the characteristic cone (i.e. the whole interior of this cone is a lacuna of the equation). Physically this means the sharpness of the transmission of the signals described by this equation, which of course is extremely important in real situations. The problem of the description of all second-order hyperbolic equations satisfying the Huygens Principle (known as the Hadamard Problem) is one of the most interesting problems in this area, which still remains open.
Recently it has been shown that the Hadamard Problem is closely related to the classification of some special configurations of hyperplanes in Euclidean space. This relation and some results towards such a classification will be discussed in the talk.