Geometric Topology (embedding theory, links modulo knots, combinatorial topology and its foundations, resolution of singularities) Algebraic Topology of metrizable spaces and 0-dimensional groups
Foundations of Mathematics (homotopy type theory, conservative extensions of intuitionistic logic, semantics of the meta-logic of first-order logics)
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) and another Ph.D. (k.f.-m.n.) from Steklov Math. Institute (2004); the two dissertations have no overlap in content.
From 2005: Research Fellow at Steklov Math. Institute, Moscow (Senior R.F. from 2008). Held visiting positions at The University of Tennessee (2007–08), Dartmouth College (Fall 2012), Institute for Advanced Study (2013).
Awards include: Möbuis Contest Prize of the Independent University of Moscow (2000) 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
Sergey A. Melikhov, “A note on O. Frolkina's paper “Pairwise disjoint Moebius bands in space””, J. Knot. Theor. Ramif., 28:7 (2019), 1971001 , 3 pp., arXiv: 1810.04089
2018
2.
S. A. Melikhov, “Immersions of the circle into a surface”, Sb. Math., 209:4 (2018), 503–518
3.
S. A. Melikhov, Algebraic topology of Polish spaces: I. Fine shape, 2018 , 20 pp., arXiv: 1808.10228
4.
S. A. Melikhov, Algebraic topology of Polish spaces. II: Axiomatic homology, 2018 , 24 pp., arXiv: 1808.10243
5.
S. A. Melikhov, Lim colim versus colim lim. I, 2018 , 44 pp., arXiv: 1809.00023
6.
S. A. Melikhov, Lim colim versus colim lim. II: Derived limits over a pospace, 2018 , 30 pp., arXiv: 1809.00022
7.
S. A. Melikhov, “Self $C_2$-equivalence of two-component links and invariants of link maps”, J. Knot. Theory Ram., 27:13 (2018), 1842012 , 22 pp., arXiv: 1711.03514
8.
Sergey A. Melikhov, “A triple-point Whitney trick”, J. Topol. Anal., 2018, 1–6 (Published online)
2017
9.
P. M. Akhmetiev, S. A. Melikhov, Projected and near-projected embeddings, 2017 , 18 pp., arXiv: 1711.03520
10.
S. A. Melikhov, Lifting generic maps to embeddings, 2017 , 15 pp., arXiv: 1711.03518
11.
S. A. Melikhov, “Topologiya dokazatelstv”, Konkurs Mëbiusa glazami ego pobeditelei, MTsNMO, Moskva, 2017, 28–33www.mccme.ru/free-books/moebius20.pdf
2015
12.
S. A. Melikhov, “Transverse Fundamental Group and Projected Embeddings”, Proc. Steklov Inst. Math., 290 (2015), 155–165 , arXiv: 1505.00505
13.
S. A. Melikhov, Mathematical semantics of intuitionistic logic, 2015/17 , 179 pp., arXiv: 1504.03380v3
14.
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. II: Semantics, 2015/18 , 35 pp., arXiv: 1504.03379v4
2013
15.
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
16.
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. I: Syntax, 2013/17 , 47 pp., arXiv: 1312.2575v4
2012
17.
S. Melikhov, Combinatorics of combinatorial topology, 2012/18 , 72 pp., arXiv: 1208.6309v2
2011
18.
S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
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)
2007
23.
S. A. Melikhov, Gauss-type formulas for link map invariants, 2007 , 21 pp., arXiv: 1711.03530
2006
24.
S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
2005
25.
S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. II. Comparison”, J. Knot Theory Ramifications, 14:5 (2005), 603–626 , arXiv: math.GT/0103114
26.
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: 2) (cited: 1) (cited: 4)
2004
27.
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)
28.
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)
29.
S. A. Melikhov, “Sphere Eversions and Realization of Mappings”, Proc. Steklov Inst. Math., 247 (2004), 143–163 , arXiv: math.GT/0305158
2003
30.
S. A. Melikhov, Colored finite type invariants and a multi-variable analogue of the Conway polynomial, 2003 , 23 pp., arXiv: math.GT/0312007
2002
31.
S. A. Melikhov, “On maps with unstable singularities”, Topology Appl., 120:1–2 (2002), 105–156 , arXiv: math.GT/0101047 (cited: 4) (cited: 4) (cited: 5)
32.
S. A. Melikhov, R. V. Mikhailov, n-quasi-isotopy: III. Engel conditions, 2002/03 , 24 pp., arXiv: math.GT/0201022v4
2001
33.
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
34.
S. A. Melikhov, “Pseudohomotopy implies homotopy for singular links of codimension $\geqslant 3$”, Russian Math. Surveys, 55:3 (2000), 589–590 (cited: 2) (cited: 1)
2003
35.
P. M. Akhmet'ev, S. A. Melikhov, “On isotopic realizability of continuous mappings”, J. Math. Sci. (N. Y.), 113:6 (2003), 759–776
1998
36.
S. A. Melikhov, Singular link concordance implies link homotopy in codimension $\ge 3$, 1998 , 12 pp., arXiv: 1810.08299
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
11.
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
27.
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
2019
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