Automorphisms of Algebras, Multiple Orthogonal Analogs of Classical Orthogonal Polynomials and Bi-orthogonal Ensembles
Emil Horozov has earned his M. Sc. Degree from Sofia University in 1973 and PhD from Moscow State University in 1978 under the supervision of V.I. Arnold. He is a full professor at Sofia University. Professor E. Horozov is a corresponding member of the Bulgarian Academy of Sciences.
His early interests have been in the bifurcation theory and the theory of limit cycles. His Ph.D. thesis contains major results of codimension 2 bifurcations of periodic solutions (“Mathematical Events of the Twentieth Century”, Springer, 2006). In the same area, together with L. Gavrilov and I. Iliev he obtained the only sharp estimate for the number of limit cycles in the Hilbert-Arnold (Gavrilov-Horozov-Iliev theorem, see Normal Forms, Bifurcations and Finiteness Problems in Differential Equations). In classical mechanics he proved the nondegeneracy of the energy-momentum map for the spherical pendulum, which allows to apply KAM theory to it. The result is known as Horozov’s theorem (R. Cushman, L. Bates, Global Aspects of Classical Integrable Systems, Birkhauser, 2015). In the bispectral problem he, together with his students and other collaborators, has obtained the most general classification results. Also this research pointed to deep connections with integrable systems and representation theory. Ideas of these studies led him to construction of broad families of multiple orthogonal polynomials, which are eigenfunctions of differential operators. In this way he extended many of the properties of the classical orthogonal polynomials to new polynomial systems. He has held visiting positions in a number of universities in USA, France, Germany, Belgium, The Netherlands, etc. Several of his students continued their studies in some of the leading world universities – MIT, UC, Berkley, Courant Insitute, etc.