Persons: Melikhov, Sergey Aleksandrovich

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Melikhov, Sergey Aleksandrovich

Statistics
in MathSciNet:	21 (20)
in zbMATH:	15 (15)
in Web of Science:	16 (15)
in Scopus:	17 (17)

Senior Researcher

Candidate of physico-mathematical sciences (2004)

Speciality:

01.01.04 (Geometry and topology)

E-mail:

UDC:

515.162, 515.163, 515.164, 515.123.4, 515.125, 515.142.26, 515.148

MSC:

57M, 57N, 57Q

Subject:

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

https://www.mathnet.ru/eng/person9152

https://scholar.google.com/citations?user=xQpf2SEAAAAJ&hl=en

https://zbmath.org/authors/ai:melikhov.sergey-a

https://mathscinet.ams.org/mathscinet/MRAuthorID/666677

https://elibrary.ru/author_items.asp?authorid=14016

https://orcid.org/0000-0001-6833-8292

https://www.webofscience.com/wos/author/record/Q-4828-2016

https://www.scopus.com/authid/detail.url?authorId=7004334864

https://www.researchgate.net/profile/Sergey_Melikhov

https://arxiv.org/a/melikhov_s_1

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	S. A. Melikhov, “The van Kampen Obstruction and Its Relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176 , arXiv: math.GT/0612082
2.	S. A. Melikhov, “Sphere Eversions and Realization of Mappings”, Proc. Steklov Inst. Math., 247 (2004), 143–163 , arXiv: math.GT/0305158
3.	S. A. Melikhov, “Steenrod homotopy”, Russian Math. Surveys, 64:3 (2009), 469–551 , arXiv: 0812.1407
4.	P. M. Akhmet'ev, S. A. Melikhov, “On isotopic realizability of continuous mappings”, J. Math. Sci. (N. Y.), 113:6 (2003), 759–776
5.	S. A. Melikhov, “On maps with unstable singularities”, Topology Appl., 120:1–2 (2002), 105–156 , arXiv: math.GT/0101047	5 ^[x]
6.	S. A. Melikhov, “Pseudohomotopy implies homotopy for singular links of codimension $\geqslant 3$”, Russian Math. Surveys, 55:3 (2000), 589–590
7.	S. A. Melikhov, “Transverse Fundamental Group and Projected Embeddings”, Proc. Steklov Inst. Math., 290 (2015), 155–165 , arXiv: 1505.00505
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	4 ^[x]
9.	S. A. Melikhov, “Isotopic and continuous realizability of maps in the metastable range”, Sb. Math., 195:7 (2004), 983–1016
10.	S. A. Melikhov, “A triple-point Whitney trick”, J. Topol. Anal., 12:4 (2020), 1041–1046 , arXiv: 2210.04016	3 ^[x]
11.	S. A. Melikhov, R. V. Mikhailov, “Links modulo knots and the isotopic realization problem”, Russian Math. Surveys, 56:2 (2001), 414–415
12.	S. A. Melikhov, “A joint logic of problems and propositions”, Doklady Math., 109:2 (2024), 130–139
13.	S. A. Melikhov, “Lifting generic maps to embeddings. Triangulation and smoothing”, Stud. Sci. Math. Hung., 59:2 (2022), 124–141 , arXiv: 2011.01402	1 ^[x]
14.	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	1 ^[x]
15.	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	1 ^[x]
16.	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	1 ^[x]
17.	S. A. Melikhov, D. Repovš, “$n$-Quasi-isotopy. II. Comparison”, J. Knot Theory Ramifications, 14:5 (2005), 603–626 , arXiv: math.GT/0103114	1 ^[x]
18.	S. A. Melikhov, “On isotopic realizability of maps factored through a hyperplane”, Sb. Math., 195:8 (2004), 1117–1163
19.	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, 237–288 , arXiv: 1711.03518
20.	S. A. Melikhov, Local knots and the prime factorization of links, 2025 , 10 pp., J. Knot Theory Ram. (to appear), arXiv: 2511.19579
21.	S. A. Melikhov, “Satellites and invariants of links”, Geometriya i Topologiya. 14, Zap. nauch. sem. POMI, 2025, 50 str. (to appear)
22.	S. A. Melikhov, Two-variable Conway polynomial and Cochran's derived invariants, 2024 , 36 pp., arXiv: math.GT/0312007v3
23.	S. A. Melikhov, Is every knot isotopic to the unknot?, 2024 , 61 pp., arXiv: 2406.09365
24.	S. A. Melikhov, Topological isotopy and finite type invariants, 2024 , 50 pp., arXiv: 2406.09331
25.	S. A. Melikhov, A Galois connection between classical and intuitionistic logics. I: Syntax, 2022 , 47 pp., arXiv: 1312.2575v5
26.	S. Melikhov, Infinite-dimensional uniform polyhedra, 2022 , 47 pp., arXiv: 1109.0346v4
27.	S. Melikhov, Metrizable uniform spaces, 2022 , 161 pp., arXiv: 1106.3249v6
28.	S. A. Melikhov, A Galois connection between classical and intuitionistic logics. II: Semantics, 2022 , 40 pp., arXiv: 1504.03379v5
29.	S. A. Melikhov, Fine shape. I, 2022 , 46 pp., arXiv: 1808.10228v2
30.	S. A. Melikhov, Lim colim versus colim lim. I, 2022 , 29 pp., arXiv: 1809.00023v3
31.	S. A. Melikhov, Lim colim versus colim lim. II: Derived limits over a pospace, 2022 , 29 pp., arXiv: 1809.00022v2
32.	S. A. Melikhov, “Embeddability of joins and products of polyhedra”, Topol. Methods Nonlinear Anal., 60:1 (2022), 185–201 , arXiv: 2210.04015
33.	S. A. Melikhov, Coronated polyhedra and coronated ANRs, 2022 , 25 pp., arXiv: 2211.09951
34.	S. A. Melikhov, Fine shape II: A Whitehead-type theorem, 2022 , 33 pp., arXiv: 2211.11102
35.	S. A. Melikhov, Fine shape III: $\Delta$-spaces and $\nabla$-spaces, 2022 , 25 pp., arXiv: 2211.11101
36.	S. A. Melikhov, Topology of Metric Spaces, ResearchGate, 2022 , 254 pp.
37.	P. M. Akhmetiev, S. A. Melikhov, “Projected and near-projected embeddings”, J. Math. Sci, 255:2 (2021), 155–174
38.	S. Melikhov, Combinatorics of combinatorial topology, 2018 , 72 pp., arXiv: 1208.6309v2
39.	S. A. Melikhov, “Immersions of the circle into a surface”, Sb. Math., 209:4 (2018), 503–518
40.	S. A. Melikhov, Algebraic topology of Polish spaces. II: Axiomatic homology, 2018 , 24 pp., arXiv: 1808.10243
41.	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
42.	S. A. Melikhov, Mathematical semantics of intuitionistic logic, 2017 , 179 pp., arXiv: 1504.03380v3
43.	S. A. Melikhov, “Topologiya dokazatelstv”, Konkurs Mëbiusa glazami ego pobeditelei, MTsNMO, Moskva, 2017, 28–33 www.mccme.ru/free-books/moebius20.pdf
44.	S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
45.	S. A. Melikhov, Gauss-type formulas for link map invariants, 2007 , 21 pp., arXiv: 1711.03530
46.	S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
47.	S. A. Melikhov, R. V. Mikhailov, n-quasi-isotopy: III. Engel conditions, 2003 , 24 pp., arXiv: math.GT/0201022v4
48.	S. A. Melikhov, Singular link concordance implies link homotopy in codimension $\ge 3$, 1998 , 12 pp., arXiv: 1810.08299
49.	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

Presentations in Math-Net.Ru

1.	Satellites and invariants of links S. A. Melikhov Conference "Low-dimensional topology 2025" November 6, 2025 11:15
2.	Spaces whose homology behaves similarly to cohomology of local compacta S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar October 22, 2025 18:25
3.	A solenoidal invariant of links of 3 and more components S. A. Melikhov Geometric Topology Seminar May 16, 2025 16:00
4.	On the geometry of the Alexander polynomial II S. A. Melikhov Geometric Topology Seminar December 23, 2024 17:20
5.	On the Cochran pairing II S. A. Melikhov Geometric Topology Seminar November 11, 2024 17:00
6.	On the Cochran pairing S. A. Melikhov Geometric Topology Seminar October 14, 2024 16:20
7.	On the geometry of the Alexander polynomial S. A. Melikhov Geometric Topology Seminar September 16, 2024 16:20
8.	Is every knot isotopic to the unknot? S. A. Melikhov Beijing–Moscow Mathematics Colloquium June 21, 2024 12:00
9.	Are isotopic PL links PL isotopic? (part IV) [talk in English] S. A. Melikhov Geometric Topology Seminar May 13, 2024 17:00
10.	Are isotopic PL links PL isotopic? (part III) [talk in English] S. A. Melikhov Geometric Topology Seminar May 6, 2024 17:00
11.	Are isotopic PL links PL isotopic? (part II) [talk in English] S. A. Melikhov Geometric Topology Seminar April 27, 2024 17:00
12.	Are isotopic PL links PL isotopic? [talk in English] S. A. Melikhov Geometric Topology Seminar April 22, 2024 17:00
13.	Extending knot isotopies to two-component links with linking number one, part III [talk in English] S. A. Melikhov Geometric Topology Seminar April 1, 2024 17:00
14.	Extending knot isotopies to two-component links with linking number one, part II [talk in English] S. A. Melikhov Geometric Topology Seminar March 25, 2024 17:00
15.	Extending knot isotopies to two-component links with linking number one [talk in English] S. A. Melikhov Geometric Topology Seminar March 18, 2024 17:00
16.	A new proof of Jin's theorem expessing Cochran's derived invariants in terms of the two-variable Conway polynomial (continued) S. A. Melikhov Geometric Topology Seminar January 29, 2024 17:00
17.	A new proof of Jin's theorem expessing Cochran's derived invariants in terms of the two-variable Conway polynomial S. A. Melikhov Geometric Topology Seminar January 22, 2024 17:00
18.	Is any knot isotopic to a unknot? S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar November 28, 2023 16:45
19.	The Conway potential function and the Rolfsen Problem. III S. A. Melikhov Geometric Topology Seminar September 20, 2023 17:00
20.	The Conway potential function and the Rolfsen Problem. II S. A. Melikhov Geometric Topology Seminar September 13, 2023 17:00
21.	The Conway potential function and the Rolfsen Problem. I S. A. Melikhov Geometric Topology Seminar September 6, 2023 17:00
22.	Projected embeddings II S. A. Melikhov Geometric Topology Seminar May 10, 2023 17:00
23.	Is every knot isotopic to a PL knot? (Cancelled) S. A. Melikhov Geometric Topology Seminar February 22, 2023 18:00
24.	Topological isotopy and the generalized Sato–Levine invariant [talk in English] S. A. Melikhov Geometric Topology Seminar February 3, 2023 16:20
25.	New results on limits, colimits and derived limits of abelian groups with applications to topology S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar November 29, 2022 16:45
26.	Links modulo knots: 5. Conway polynomial, colored Conway polynomial and the geometry of the coefficients of their reduced versions S. A. Melikhov Geometric Topology Seminar April 20, 2022 17:00
27.	Links modulo knots: 4. Kirk's invariant and its relation with Cochran's invariants S. A. Melikhov Geometric Topology Seminar April 13, 2022 17:00
28.	Links modulo knots: 3. Cochran's derived invariants and Kojima's $\eta$-function S. A. Melikhov Geometric Topology Seminar April 6, 2022 17:00
29.	Links modulo knots: 2. Ornaments in the critical dimension S. A. Melikhov Geometric Topology Seminar March 30, 2022 17:00
30.	Links modulo knots: 1. The linking number and the triple $\bar\mu$-invariant S. A. Melikhov Geometric Topology Seminar March 23, 2022 17:00
31.	Topological isotopy and Cochran's invariants of links S. A. Melikhov Mathematical Colloquium of the Bauman Moscow State Technical University March 3, 2022 17:30
32.	Do there exist cophantom phantoms? S. A. Melikhov Geometric Topology Seminar December 24, 2021 17:00
33.	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
34.	Slim shape S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar October 19, 2021 16:45
35.	Metric polyhedra and projective cubes S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar February 18, 2020 16:45
36.	Injective metric and cubical collapsing S. A. Melikhov Geometric Topology Seminar October 16, 2019 17:00
37.	Cubical collapsing and injective metric S. A. Melikhov Geometric Topology Seminar October 9, 2019 17:00
38.	Link maps in $S^4$ and their applications to links in $S^3$ S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar September 17, 2019 16:45
39.	Is every knot isotopic to the unknot? S. A. Melikhov Geometric Topology Seminar September 11, 2019 17:00
40.	Brunnian link maps in the 4-sphere and Goussarov-Habiro moves on links in the 3-sphere S. A. Melikhov Geometric Topology Seminar May 21, 2019 16:00
41.	Brunnian link maps in the 4-sphere and the Chinese Rings puzzle S. A. Melikhov Geometric Topology Seminar December 17, 2018 15:30
42.	Corrected derived limits, or How to expel set theory from algebraic topology (part II) S. A. Melikhov Geometric Topology Seminar October 1, 2018 15:30
43.	Functors lim^p and algebraic topology of separable metric spaces S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar September 25, 2018 16:45
44.	Corrected derived limits, or How to expel set theory from algebraic topology S. A. Melikhov Geometric Topology Seminar September 24, 2018 15:30
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
46.	Lim colim versus colim lim S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar April 24, 2018 16:45
47.	Limit of colimits versus colimit of limits II S. A. Melikhov Geometric Topology Seminar April 12, 2018 14:00
48.	Limit of colimits versus colimit of limits S. A. Melikhov Geometric Topology Seminar April 5, 2018 14:00
49.	Projected embeddings and approximation of maps by embeddings S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar November 28, 2017 16:45
50.	Projected embeddings for PL and smooth maps S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar November 7, 2017 16:45
51.	Projected embeddings S. A. Melikhov Geometric Topology Seminar October 26, 2017 14:00
52.	Kolmogorov's interpretation and a formal semantics of the meta-logic of intuitionistic logic S. Melikhov Workshop on Proof Theory, Modal Logic and Reflection Principles October 17, 2017 17:15
53.	On $\Delta$-link homotopy Yuka Kotorii, S. A. Melikhov Geometric Topology Seminar August 31, 2017 17:00
54.	Fine shape and uniqueness theorems for homology and cohomology of Polish spaces S. A. Melikhov Geometric Topology Seminar August 10, 2017 14:00
55.	$\Delta$-link homotopy of links in $S^3$ and invariants of link maps in $S^4$ S. A. Melikhov Geometric Topology Seminar July 20, 2017 15:00
56.	Семантика металогики. (Часть 2) S. A. Melikhov Seminars "Proof Theory" and "Logic Online Seminar" March 6, 2017 18:30
57.	Семантика металогики. (Часть 1) S. A. Melikhov Seminars "Proof Theory" and "Logic Online Seminar" February 27, 2017 18:30
58.	Формальная металогика логик первого порядка и её формальная семантика S. A. Melikhov Seminars "Proof Theory" and "Logic Online Seminar" May 16, 2016
59.	О независимых принципах в совместной логике задач и высказываний. Часть 2 S. A. Melikhov Seminars "Proof Theory" and "Logic Online Seminar" October 5, 2015 18:30
60.	О независимых принципах в совместной логике задач и высказываний. Часть 1 S. A. Melikhov Seminars "Proof Theory" and "Logic Online Seminar" September 28, 2015 18:30
61.	A joint logic of problems and propositions S. A. Melikhov "Algorithmic problems in algebra and logic" (S.I.Adian seminar) March 4, 2014 18:30
62.	A joint logic of problems and propositions S. A. Melikhov "Algorithmic problems in algebra and logic" (S.I.Adian seminar) February 25, 2014 18:30
63.	A problem of Kolmogorov, and sheaves S. A. Melikhov Geometric Topology Seminar October 22, 2013 15:00
64.	On topology of solutions of problems S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar October 1, 2013 16:45
65.	Combinatorics of collapsible polyhedra and maps S. A. Melikhov Geometric Topology Seminar April 17, 2012 15:00
66.	On geometry of the index $8$ subgroup of the third stable stem S. A. Melikhov Geometric Topology Seminar November 1, 2011 15:30
67.	Uniform polyhedra S. A. Melikhov Geometric Topology Seminar July 21, 2011 14:30
68.	Uniform polyhedra S. A. Melikhov Geometric Topology Seminar June 15, 2011 18:00
69.	The combinatorial viewpoint in algebraic K-theory of spaces S. A. Melikhov Geometric Topology Seminar April 19, 2011 15:00
70.	Combinatorial metods in theory of embeddings S. A. Melikhov Knots and Representation Theory April 5, 2011 18:30

Organisations