Geometric topology, including: combinatorial topology and its foundations; links (modulo knots); topology of 2-polyhedra; piecewise-linear and topological embeddings; resolution of singularities of smooth maps and lifting of maps to embeddings; algebraic topology of Polish spaces and 0-dimensional groups.
Graduated from Lomonosov Moscow State University (2001) and from a math class at Moscow State 57th School (1996).
Ph.D. from University of Florida (2005, adviser A. N. Dranishnikov) and another Ph.D. (k.f.-m.n.) from Steklov Math. Institute (2004, adviser E. V. Shchepin); the two dissertations have no overlap in content.
From 2005: Research Fellow at Steklov Math. Institute, Moscow (Senior R.F. from 2008). In 2007–08 was a Visiting Assistant Professor at University of Tennessee.
Awards received include Möbuis Contest Prize (2000, Independent University of Moscow) and Russian Academy of Sciences Medal for Young Scientists (2006).
S. A. Melikhov, “Steenrod homotopy”, Russian Math. Surveys, 64 (2009), 469–551, arXiv: 0812.1407
S. A. Melikhov, “The van Kampen obstruction and its relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176, arXiv: math.GT/0612082
S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. I. Questions of nilpotence”, J. Knot Theory Ramifications, 14:5 (2005), 571–602, arXiv: math.GT/0103113
S. A. Melikhov, “Sphere eversions and realization of mappings”, Proc. Steklov Inst. Math., 247 (2004), 143–163, arXiv: math.GT/0305158
S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
S. Melikhov, “Direct limit of inverse limits versus inverse limit of direct limits”, 25th Summer Conf. on Topol. and Appl. (July 25–30, 2010, Jan Kochanowski Univ., Kielce, Poland), Topology Atlas, 2010, Document # cbat-69link
S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. II. Comparison”, J. Knot Theory Ramifications, 14:5 (2005), 603–626 , arXiv: math.GT/0103114
S. A. Melikhov, R. V. Mikhailov, n-quasi-isotopy: III. Engel conditions, 2003 , 24 pp., arXiv: math.GT/0201022
S. A. Melikhov, Colored finite type invariants and a multi-variable analogue of the Conway polynomial, 2003 , 23 pp., arXiv: math.GT/0312007
Presentations in Math-Net.Ru
Lim colim versus colim lim Sergey A. Melikhov International conference "Algebraic Topology, Combinatorics, and Mathematical Physics" on occasion of Victor Buchstaber's 75th birthday May 24, 2018 17:00
Lim colim versus colim lim S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar April 24, 2018 16:45