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, A Galois connection between classical and intuitionistic logics. II: Semantics, 2022 , 40 pp., arXiv: 1504.03379v5
5.
S. A. Melikhov, Fine shape. I, 2022 , 46 pp., arXiv: 1808.10228v2
6.
S. A. Melikhov, Lim colim versus colim lim. I, 2022 , 29 pp., arXiv: 1809.00023v3
7.
S. A. Melikhov, Lim colim versus colim lim. II: Derived limits over a pospace, 2022 , 29 pp., arXiv: 1809.00022v2
8.
S. A. Melikhov, “Embeddability of joins and products of polyhedra”, Topol. Methods Nonlinear Anal., 60:1 (2022), 185–201 , arXiv: 2210.04015;
9.
S. A. Melikhov, “Lifting generic maps to embeddings. Triangulation and smoothing”, Stud. Sci. Math. Hung., 59:2 (2022), 124–141 , arXiv: 2011.01402;
10.
S. A. Melikhov, Coronated polyhedra and coronated ANRs, 2022 , 25 pp., arXiv: 2211.09951
11.
S. A. Melikhov, Fine shape II: A Whitehead-type theorem, 2022 , 33 pp., arXiv: 2211.11102
12.
S. A. Melikhov, Fine shape III: $\Delta$-spaces and $\nabla$-spaces, 2022 , 25 pp., arXiv: 2211.11101
13.
S. A. Melikhov, Topology of Metric Spaces, https://www.researchgate.net/publication/365476532_Topology_of_Metric_Spaces, 2022 , 254 pp.
14.
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
15.
S. A. Melikhov, Lifting generic maps to embeddings: II. The double point obstruction, 2021 , 40 pp., arXiv: 1711.03518v6
16.
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
19.
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
20.
S. Melikhov, Combinatorics of combinatorial topology, 2018 , 72 pp., arXiv: 1208.6309v2
21.
S. A. Melikhov, “Immersions of the circle into a surface”, Sb. Math., 209:4 (2018), 503–518
22.
S. A. Melikhov, Algebraic topology of Polish spaces. II: Axiomatic homology, 2018 , 24 pp., arXiv: 1808.10243
23.
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
24.
S. A. Melikhov, Mathematical semantics of intuitionistic logic, 2017 , 179 pp., arXiv: 1504.03380v3
25.
S. A. Melikhov, “Topologiya dokazatelstv”, Konkurs Mëbiusa glazami ego pobeditelei, MTsNMO, Moskva, 2017, 28–33www.mccme.ru/free-books/moebius20.pdf
2015
26.
S. A. Melikhov, “Transverse Fundamental Group and Projected Embeddings”, Proc. Steklov Inst. Math., 290 (2015), 155–165 , arXiv: 1505.00505
2013
27.
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
28.
S. A. Melikhov, Combinatorics of embeddings, 2011 , 49 pp., arXiv: 1103.5457
2009
29.
S. A. Melikhov, “Steenrod homotopy”, Russian Math. Surveys, 64:3 (2009), 469–551 , arXiv: 0812.1407
30.
S. A. Melikhov, “The van Kampen Obstruction and Its Relatives”, Proc. Steklov Inst. Math., 266 (2009), 142–176 , arXiv: math.GT/0612082
2007
31.
S. A. Melikhov, Gauss-type formulas for link map invariants, 2007 , 21 pp., arXiv: 1711.03530
2006
32.
S. A. Melikhov, E. V. Shchepin, The telescope approach to embeddability of compacta, 2006 , 26 pp., arXiv: math.GT/0612085
2005
33.
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
30.
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
42.
Lim colim versus colim lim S. A. Melikhov Algebraic topology and its applications. Postnikov memorial seminar April 24, 2018 16:45
2022
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