Home PageFyodor Tkachov's claims to fame

(Differential-) Algebraic algorithms for loop calculations (since 1980)
"Nowadays the technique probably more popularly used for calculating the contribution of Feynman diagrams is that based on the integration-by-parts in D dimensions..." integration-by-parts in D dimensions (1981-1983)
hot topic "algorithm of algorithms" for multiloop calculations (1996)

Asymptotic operation (since March 1981)   
the break... Extension Principle (1981) 
...through OPE with massless particles (1982, 1983) 
 efficient calculational formulae for OPE (1983; with S.Gorishny and S.Larin)
seriously great Euclidean asymptotic operation including mass expansions (1982-1986; parts with G.Pivovarov)
"fascinating reading ... outstanding" mathematical theory of asymptotic operation (1986-1988; with A.Kuznetsov and V.Vlasov)
insanely great non-Euclidean asymptotic operation
 systematic perturbation theory with unstable fields (since 1998)
hot topic systematic approach to factorization theorems of pQCD (since 2000)

Data processing (since Dec. 1992) 
hot topic Optimal Jet Definition (1999; more); see also the Jet Energy Flow Project (Snowmass, 2001)
 belongs to any textbook of mathematical statistics Quasi-optimal weights (2000; 2006)

Physics applications    
 NNLO QCD correction to total cross section of e+e- into hadrons (1979, with K.Chetyrkin and A.Kataev)
 5-loop renormalization group calculations in the scalar phi^4 model (1981-1983, with K.Chetyrkin, S.Gorishny and S.Larin)
 NNLO QCD corrections to DIS structure functions (1991, with S.Larin and J.Vermaseren)
"A particularly powerful (and unusual) variable is the average jet count ... inspired by the work of Tkachov" a contribution to observation of the top quark at D0/Fermilab
 Two-loop corrections to heavy-to-light decays (2004, with I. Blokland, A. Czarnecki and M. Slusarczyk)

Software projects 
 design of MINCER (1981; implementation with S.Gorishny and S.Larin)
BEAR = Basic Extensible Algebra Resource (since 1997; more)
   small but sweet hyper-efficient algorithm for Dirac traces in D dimensions (1998)
hot topic Optimal Jet Finder (2000-2003, with D.Yu.Grigoriev and E.Jankowski; final public release)
 POUZYRY: a novel class of algorithms for modelling functions from a (quasi) random sample (since 2003)

Educational projects 
 Oberon Day @ CERN (10 March 2004)
Informatica-21