The main directions of I. A. Panin's work are the theory of oriented cohomology on
algebraic varieties, algebraic K-theory of homogeneous varieties, Gersten's conjecture, the Grothendieck-Serre conjecture on
principal G-bundles, and
purity in algebraic geometry. and Riemann-Roch type theorems for the
Adams operation. Panin found a proof of Gersten's conjecture in the case of equal characteristic and an affirmative solution (jointly with Manuel Ojanguren) of the "purity" problem for quadratic forms. concerning index reduction formulas for the function fields of involution varieties. ==Selected publications==