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
Born in 1980. 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, “Topological isotopy and Cochran’s derived invariants”, Topology, Geometry, and Dynamics: V. A. Rokhlin Memorial, Contemporary Mathematics, 772, eds. A. M. Vershik, V. M. Buchstaber, A. V. Malyutin, Amer. Math. Soc., Providence, RI, 2021, 249–266 arXiv: 2011.01409
S. A. Melikhov, “Lifting generic maps to embeddings. The double point obstruction”, Essays on Topology. Dedicated to Valentin Poénaru, eds. L. Funar and A. Papadopoulos, Springer, 2025, 46 pp. (to appear) arXiv: 1711.03518
2024
2.
S. A. Melikhov, Two-variable Conway polynomial and Cochran's derived invariants, 2024 , 36 pp., arXiv: math.GT/0312007v3
3.
S. A. Melikhov, “A joint logic of problems and propositions”, Doklady Math., 109:2 (2024), 130–139
4.
S. A. Melikhov, Is every knot isotopic to the unknot?, 2024 , 61 pp., arXiv: 2406.09365
5.
S. A. Melikhov, Topological isotopy and finite type invariants, 2024 , 52 pp., arXiv: 2406.09331
2022
6.
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. I: Syntax, 2022 , 47 pp., arXiv: 1312.2575v5
S. A. Melikhov, A Galois connection between classical and intuitionistic logics. II: Semantics, 2022 , 40 pp., arXiv: 1504.03379v5
10.
S. A. Melikhov, Fine shape. I, 2022 , 46 pp., arXiv: 1808.10228v2
11.
S. A. Melikhov, Lim colim versus colim lim. I, 2022 , 29 pp., arXiv: 1809.00023v3
12.
S. A. Melikhov, Lim colim versus colim lim. II: Derived limits over a pospace, 2022 , 29 pp., arXiv: 1809.00022v2
13.
S. A. Melikhov, “Embeddability of joins and products of polyhedra”, Topol. Methods Nonlinear Anal., 60:1 (2022), 185–201 , arXiv: 2210.04015;
14.
S. A. Melikhov, “Lifting generic maps to embeddings. Triangulation and smoothing”, Stud. Sci. Math. Hung., 59:2 (2022), 124–141 , arXiv: 2011.01402;
15.
S. A. Melikhov, Coronated polyhedra and coronated ANRs, 2022 , 25 pp., arXiv: 2211.09951
16.
S. A. Melikhov, Fine shape II: A Whitehead-type theorem, 2022 , 33 pp., arXiv: 2211.11102
17.
S. A. Melikhov, Fine shape III: $\Delta$-spaces and $\nabla$-spaces, 2022 , 25 pp., arXiv: 2211.11101
18.
S. A. Melikhov, Topology of Metric Spaces, ResearchGate, 2022 , 254 pp.
19.
V. I. Buslaev, V. M. Buchstaber, A. N. Dranishnikov, V. M. Kliatskine, S. A. Melikhov, L. Montejano, S. P. Novikov, P. V. Semenov, “Evgenii Vital'evich Shchepin (on his 70th birthday)”, Russian Math. Surveys, 77:3 (2022), 559–569
2021
20.
S. A. Melikhov, “Topological isotopy and Cochran's derived invariants”, Topology, Geometry, and Dynamics: V. A. Rokhlin Memorial, Contemp. Math., 772, Amer. Math. Soc., Providence, RI, 2021, 249–266 , arXiv: 2011.01409
P. M. Akhmetiev, S. A. Melikhov, “Projected and near-projected embeddings”, J. Math. Sci, 255:2 (2021), 155–174
2019
23.
S. A. Melikhov, “A note on O. Frolkina`s paper “Pairwise disjoint Moebius bands in space””, J. Knot Theory Ramif., 28:7 (2019), 1971001 , 3 pp., arXiv: 1810.04089
2018
24.
S. Melikhov, Combinatorics of combinatorial topology, 2018 , 72 pp., arXiv: 1208.6309v2
25.
S. A. Melikhov, “Immersions of the circle into a surface”, Sb. Math., 209:4 (2018), 503–518
26.
S. A. Melikhov, Algebraic topology of Polish spaces. II: Axiomatic homology, 2018 , 24 pp., arXiv: 1808.10243
27.
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
2017
28.
S. A. Melikhov, Mathematical semantics of intuitionistic logic, 2017 , 179 pp., arXiv: 1504.03380v3
29.
S. A. Melikhov, “Topologiya dokazatelstv”, Konkurs Mëbiusa glazami ego pobeditelei, MTsNMO, Moskva, 2017, 28–33www.mccme.ru/free-books/moebius20.pdf
2015
30.
S. A. Melikhov, “Transverse Fundamental Group and Projected Embeddings”, Proc. Steklov Inst. Math., 290 (2015), 155–165 , arXiv: 1505.00505
2013
31.
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
2011
32.
S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
2009
33.
S. A. Melikhov, “Steenrod homotopy”, Russian Math. Surveys, 64:3 (2009), 469–551 , arXiv: 0812.1407
34.
S. A. Melikhov, “The van Kampen Obstruction and Its Relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176 , arXiv: math.GT/0612082
2007
35.
S. A. Melikhov, Gauss-type formulas for link map invariants, 2007 , 21 pp., arXiv: 1711.03530
2006
36.
S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
2005
37.
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, D. Repovš, “$n$-Quasi-isotopy. I. Questions of nilpotence”, J. Knot Theory Ramifications, 14:5 (2005), 571–602 , arXiv: math.GT/0103113
Инварианты топологической изотопии S. A. Melikhov Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2021 November 24, 2021 14:40
31.
Slim shape S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar October 19, 2021 16:45
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
43.
Lim colim versus colim lim S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar April 24, 2018 16:45
2025
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