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.
Biography
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).
Main publications:
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. Melikhov, J. Zaja̧c, “Contractible polyhedra in products of trees and absolute retracts in products of dendrites”, Proc. Amer. Math. Soc., 2013 (to appear) , arXiv: 1102.0696
2.
S. Melikhov, Combinatorics of combinatorial topology, 2012, 70 pp., arXiv: 1208.6309v1
3.
S. Melikhov, Infinite-dimensional uniform polyhedra, 2011, 39 pp., arXiv: 1109.0346
4.
S. Melikhov, Metrizable uniform spaces, 2011, 77 pp., arXiv: 1106.3249
5.
S. A. Melikhov, “Steenrod homotopy”, Russian Math. Surveys, 64:3 (2009), 469–551
6.
S. A. Melikhov, “The van Kampen Obstruction and Its Relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176
7.
S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. II. Comparison”, J. Knot Theory Ramifications, 14:5 (2005), 603–626, arXiv: math.GT/0103114
8.
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
9.
S. A. Melikhov, “On isotopic realizability of maps factored through a hyperplane”, Sb. Math., 195:8 (2004), 1117–1163
10.
S. A. Melikhov, “Isotopic and continuous realizability of maps in the metastable range”, Sb. Math., 195:7 (2004), 983–1016
11.
S. A. Melikhov, “Sphere Eversions and Realization of Mappings”, Proc. Steklov Inst. Math., 247 (2004), 143–163
12.
S. A. Melikhov, “On maps with unstable singularities”, Topology Appl., 120:1–2 (2002), 105–156, arXiv: math.GT/0101047
13.
S. A. Melikhov, R. V. Mikhailov, “Links modulo knots and the isotopic realization problem”, Russian Math. Surveys, 56:2 (2001), 414–415
14.
S. A. Melikhov, “Pseudohomotopy implies homotopy for singular links of codimension $\geqslant 3$”, Russian Math. Surveys, 55:3 (2000), 589–590
15.
P. M. Akhmetev, S. A. Melikhov, “On isotopic realizability of continuous mappings”, Geometriya i topologiya. 5, Zap. nauchn. sem. POMI, 267, POMI, SPb., 2000, 53–87; P. M. Akhmet'ev, S. A. Melikhov, “On isotopic realizability of continuous mappings”, J. Math. Sci. (N. Y.), 113:6 (2003), 759–776
Terms of Use