Peter M. Akhmet'ev was preparing his Ph.D. in 1989 under Prof. M. M. Postnikov in the Moscow Steklov Mathematical Institute. His thesis was dedicated to geometrical problems in Algebraic L-theory, concerning splitting obstructions. After he start to work in Differential and Geometric Topology and Mathematical Physics. His main results are following. 1) Application of Stable Homotopy in Geometric Topology. For example, Hopf invariant one problem: an arbitrary map $S^n\to S^n$, $n\ne 2$ can be approximated by an embedding in $R^{2n}$ if $n\ne 1,3$, or $7$. 2) A number of results concerning applications of Immersion Theory in Pseudo-isotopy Theory [1]. 3) New geometrical proofs of classical results in Stable Homotopy groups of Spheres (join with P. J. Eccles and A. Szucs) [2], [3]. 4) A number of results in Mathematical Physics, concerning 3D analytical models of Electromagnetic Field and application of Link Theory in Magnetic Hydrodynamic.
Main publications:
P. M. Akhmetev, “Vlozheniya kompaktov, stabilnye gomotopicheskie gruppy sfer i teoriya osobennostei”, UMN, 55:3(333) (2000), 3–62; Russian Math. Surveys, 55:3 (2000), 405–462
P. Akhmet'ev and A. Szűcs, “Geometric proof of the easy part of the Hopf invariant one theorem”, Math. Slovaca, 49:1 (1999), 71–74
P. M. Akhmet'ev and P. J. Eccles, “A geometric proof of Browder's result on the vanishing of the Kervaire invariant”, The report at the Conference on 60-th Birthday of S. P. Novikov, Proc. Steklov Math. Inst., 225 (1999), 40–44
; Russian Math. Surveys, 55:3 (2000), 
