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. A. Melikhov, “Immersions of the circle into a surface”, Sb. Math., 209:4 (2018), 503–518
2017
2.
S. A. Melikhov, Gauss-type formulas for link map invariants, 2017 , 21 pp., arXiv: 1711.03530
3.
P. M. Akhmetiev, S. A. Melikhov, Projected and near-projected embeddings, 2017 , 18 pp., arXiv: 1711.03520
4.
S. A. Melikhov, Lifting generic maps to embeddings, 2017 , 15 pp., arXiv: 1711.03518
5.
S. A. Melikhov, Classifying two-component links in $S^3$ up to self $C_2$-equivalence via invariants of link maps in $S^4$, 2017 , 20 pp., arXiv: 1711.03514
2015
6.
S. A. Melikhov, “Transverse Fundamental Group and Projected Embeddings”, Proc. Steklov Inst. Math., 290 (2015), 155–165 , arXiv: 1505.00505
7.
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. II: Semantics, 2015 / 2017 , 34 pp., arXiv: 1504.03379v3
8.
S. A. Melikhov, Mathematical semantics of intuitionistic logic, 2015 / 2017 , 179 pp., arXiv: 1504.03380v3
2013
9.
S. Melikhov, J. Zaja̧c, “Contractible polyhedra in products of trees and absolute retracts in products of dendrites”, Proc. Amer. Math. Soc., 141:7 (2013), 2519–2535 , arXiv: 1102.0696 (cited: 1)
10.
S. Melikhov, “On topology of proofs”, 28th Summer Conf. on Topol. and Appl. (July 23–26, 2013, Nipissing Univ., North Bay, Ontario, Canada), Topology Atlas, 2013, Document # cbhq-29link
11.
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. I: Syntax, 2013 / 2017 , 47 pp., arXiv: 1312.2575v4
2012
12.
S. Melikhov, Combinatorics of combinatorial topology, 2012 , 70 pp., arXiv: 1208.6309v1
13.
S. Melikhov, “Combinatorics of collapsible polyhedra and maps”, Int. Topol. Conf. “Alexandroff Readings”. Abstracts (Moscow, May 21–25, 2012), Moscow State Univ., 2012, 48–49link
S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
2010
17.
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, “The van Kampen Obstruction and Its Relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176 , arXiv: math.GT/0612082 (cited: 6) (cited: 4) (cited: 4) (cited: 6)
2006
20.
S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
2005
21.
S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. II. Comparison”, J. Knot Theory Ramifications, 14:5 (2005), 603–626 , arXiv: math.GT/0103114
22.
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 (cited: 3) (cited: 1) (cited: 1) (cited: 3)
2004
23.
S. A. Melikhov, “On isotopic realizability of maps factored through a hyperplane”, Sb. Math., 195:8 (2004), 1117–1163 (cited: 1) (cited: 1) (cited: 1)
24.
S. A. Melikhov, “Isotopic and continuous realizability of maps in the metastable range”, Sb. Math., 195:7 (2004), 983–1016 (cited: 3) (cited: 4) (cited: 3)
25.
S. A. Melikhov, “Sphere Eversions and Realization of Mappings”, Proc. Steklov Inst. Math., 247 (2004), 143–163 , arXiv: math.GT/0305158
2003
26.
S. A. Melikhov, R. V. Mikhailov, n-quasi-isotopy: III. Engel conditions, 2003 , 24 pp., arXiv: math.GT/0201022
27.
S. A. Melikhov, Colored finite type invariants and a multi-variable analogue of the Conway polynomial, 2003 , 23 pp., arXiv: math.GT/0312007
2002
28.
S. A. Melikhov, “On maps with unstable singularities”, Topology Appl., 120:1–2 (2002), 105–156 , arXiv: math.GT/0101047 (cited: 10) (cited: 4) (cited: 4) (cited: 5)
2001
29.
S. A. Melikhov, R. V. Mikhailov, “Links modulo knots and the isotopic realization problem”, Russian Math. Surveys, 56:2 (2001), 414–415 (cited: 1) (cited: 1)
2000
30.
S. A. Melikhov, “Pseudohomotopy implies homotopy for singular links of codimension $\geqslant 3$”, Russian Math. Surveys, 55:3 (2000), 589–590 (cited: 1)
2003
31.
P. M. Akhmet'ev, S. A. Melikhov, “On isotopic realizability of continuous mappings”, J. Math. Sci. (N. Y.), 113:6 (2003), 759–776
Presentations in Math-Net.Ru
1.
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
2.
Lim colim versus colim lim S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar April 24, 2018 16:45
A joint logic of problems and propositions S. A. Melikhov Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic" March 4, 2014 18:30
18.
A joint logic of problems and propositions S. A. Melikhov Seminar of the Department of Mathematical Logic "Algorithmic problems in algebra and logic" February 25, 2014 18:30
2018
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