Arnold's seminar
April 6th, 1999

Speaker:  
Fyodor Tkachov (Institute for Nuclear Research, Russ. Acad. Sci., Moscow)

Title:  

Mathematical problems of theoretical high-energy physics and the theory of
singularities

Abstract:  

Some key problems at the bleeding edge of the modern theoretical particle
physics lead one to the mathematical theory of singularities:
(1) advanced methods of computation of so-called multiloop integrals
["algebraic algorithms for multiloop calculations", F.Tkachov et al., since
1981] involve ill-understood (especially in the constructive aspect)
generalizations of the Bernstein functional equation;
(2) advanced methods of asymptotic expansions of such integrals ["theory of
asymptotic operation", F.Tkachov et al., since 1982] involve some tricks for
treatment of singularities in the context of asymptotic expansions of
singular functions which [tricks] just beg to be embedded into a yet-to-be
developed systematic theory at the intersection of the theory of
singularities and the theory of generalized functions.