Graduated from the Moscow State University in 1997 (Faculty of computational mathematics and cybernetics, department of nonlinear dynamical systems and control processing). I defended my Ph.D. thesis in 2000. I have over 75 publications, including 3 monographs.
Main publications:
A. Yu. Savin, “On the index of elliptic operators associated with a diffeomorphism of a manifold”, Dokl. Math., 82:3 (2010), 884-886
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, Elliptic theory and noncommutative geometry. Nonlocal elliptic operators, Birkhäuser, Basel, 2008 , 224 pp.
V.E. Nazaikinskii, A.Yu. Savin, B.-W. Schulze, B.Yu. Sternin, Elliptic theory on singular manifolds, Chapman & Hall/CRC, Boca Raton, FL, 2006 , 356 pp.
A. Savin, “Elliptic operators on manifolds with singularities and $K$-homology”, K-Theory, 34:1 (2005), 71-98
A. Savin, B. Sternin, “The eta invariant and parity conditions”, Adv. Math., 182:2 (2004), 173–203
A. Savin, E. Schrohe, “Analytic and algebraic indices of elliptic operators associated with discrete groups of quantized canonical transformations”, Journal of Functional Analysis, 278:5 (2020), 108400 , 45 pp. (cited: 1)
2.
N. R. Izvarina, A. Yu. Savin, “Complexes in relative elliptic theory”, Eurasian Math. J., 11:4 (2020), 45–57;
2019
3.
D. A. Poluektova, A. Yu. Savin, B. Yu. Sternin, “On the algebra of operators corresponding to the union of smooth submanifolds”, Proceedings of the S.M. Nikolskii Mathematical Institute of RUDN University, CMFD, 65, no. 4, PFUR, M., 2019, 672–682
4.
V. E. Nazaikinskii, A. Yu. Savin, P. A. Sipailo, “Sobolev Problems with Spherical Mean Conditions and Traces of Quantized Canonical Transformations”, Russian Journal of Mathematical Physics, 26 (2019), 483–498
5.
A. Savin, E. Schrohe, B. Sternin, “Elliptic operators associated with groups of quantized canonical transformations”, Bull. Sci. Math., 155 (2019), 141–167 (cited: 2) (cited: 4)
2018
6.
A. Yu. Savin, B. Yu. Sternin, E. Schrohe, “Elliptic operators associated with groups of quantized canonical transformations”, Russian Math. Surveys, 73:3 (2018), 546–548 (cited: 2) (cited: 1)
7.
A. Yu. Savin, “On homotopic classification of elliptic problems with contractions and $K$-groups of corresponding $C^*$-algebras”, CMFD, 64, no. 1, 2018, 164–179
2017
8.
A. Savin, B. Sternin, Introduction to complex theory of differential equations, Birkhäuser, Basel, 2017 , 1-128 pp.
9.
A.Yu. Savin, B.Yu. Sternin, “Elliptic differential dilation-contraction problems on manifolds with boundary”, Differ. Equ., 53:5 (2017), 665–676
2018
10.
A. Yu. Savin, B. Yu. Sternin, “Elliptic G-Operators on Manifolds with Isolated Singularities”, Journal of Mathematical Sciences, 233 (2018), 930–948 (cited: 1)
2016
11.
A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary”, Ufa Math. Journal, 8:3 (2016), 122–129
12.
A. Yu. Savin, B. Yu. Sternin, “Ellipticheskie zadachi s rastyazheniyami-szhatiyami na mnogoobraziyakh s kraem”, Doklady akademii nauk, 469:2 (2016), 154–156
Anton Savin, Elmar Schrohe, Boris Sternin, Elliptic Operators Associated with Groups of Quantized Canonical Transformations, 2016 (Published online) , 23 pp., arXiv: arXiv:1612.02981
2020
15.
A. Yu. Savin, B. Yu. Sternin, “On Traces of Operators Associated with Actions of Compact Lie Groups”, Journal of Mathematical Sciences, 248 (2020), 647–660 , arXiv: 1612.02286
2015
16.
A. Savin, E. Schrohe, B. Sternin, “Uniformization and Index of Elliptic Operators Associated with Diffeomorphisms of a Manifold”, Russian Journal of Mathematical Physics, 22:3 (2015), “410–420” , arXiv: 1111.1525 (cited: 2) (cited: 3)
17.
A. Savin, B. Sternin, “Differential equations on complex manifolds”, Geometric Methods in Physics (XXXIII Workshop, Białowieża, Poland, June 29 – July 5, 2014), Trends in mathematics, eds. Piotr Kielanowski, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov, Springer, 2015, 273–292
2014
18.
A. Yu. Savin, B. Yu. Sternin, “Index of Sobolev problems on manifolds with many-dimensional singularities”, Differ. Equations, 50:2 (2014), 232–245 (cited: 1) (cited: 1) (cited: 1) (cited: 1)
19.
A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Doklady Mathematics, 89:1 (2014), 61-64
20.
A.Yu. Savin, B. Yu. Sternin, “Index of nonlocal problems associated with a bundle”, Differ. Equations, 50:8 (2014), 1112–1121
21.
A. Yu. Savin, B.Yu. Sternin, “Index of elliptic operators for diffeomorphisms of manifolds”, J. of Noncommutative Geometry, 8:3 (2014), 695–734 (cited: 5) (cited: 5)
2013
22.
A. Yu. Savin, B.Yu. Sternin, “Elliptic translators on manifolds with multidimensional singularities”, Differ. Equations, 49:4 (2013), 494–509 (cited: 2) (cited: 2) (cited: 3)
A.Savin, B. Sternin, “Elliptic theory for operators associated with diffeomorphisms of smooth manifolds”, Pseudo-Differential Operators, Generalized Functions and Asymptotics, Operator Theory: Advances and Applications, 231, Springer, Basel, 2013, 1–26
26.
A. Yu. Savin, B. Yu. Sternin, “Uniformization of nonlocal elliptic operators and KK-theory”, Russian Journal of Mathematical Physics, 20:3 (2013), 345–359 (cited: 5) (cited: 6)
2014
27.
A.Yu. Savin, B.Yu. Sternin, E. Schrohe, “On the Index Formula for an Isometric Diffeomorphism”, Journal of Mathematical Sciences, 201:6 (2014), 818–829
2012
28.
A. Yu. Savin, B.Yu. Sternin, “Elliptic translators on manifolds with point singularities”, Differ. Equations, 48:12 (2012), 1577–1585 (cited: 2) (cited: 1) (cited: 1) (cited: 2)
2011
29.
A.Yu. Savin, B.Yu. Sternin, “On the index of elliptic translators”, Dokl. Math., 83:1 (2011), 76-79 (cited: 2) (cited: 1) (cited: 2)
30.
A. Yu. Savin, “On the index of nonlocal elliptic operators for compact Lie groups”, Cent. Eur. J. Math., 9:4 (2011), 833-850 (cited: 2) (cited: 1) (cited: 5)
31.
A. Yu. Savin, B. Yu. Sternin, “On the index of elliptic operators for the group of dilations”, Sb. Math., 202:10 (2011), 1505–1536 (cited: 3) (cited: 1) (cited: 1) (cited: 5)
32.
A. Yu. Savin, “On the symbol of nonlocal operators in Sobolev spaces”, Differ. Equ., 47:6 (2011), 897–900 (cited: 3) (cited: 4)
33.
A.Yu. Savin, B.Yu. Sternin, “An index formula for nonlocal operators corresponding to a diffeomorphism of a manifold”, Dokl. Math., 83:3 (2011), 353–356 (cited: 1) (cited: 1) (cited: 1)
34.
A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714 (cited: 4) (cited: 2) (cited: 2) (cited: 6)
35.
A.Yu. Savin, B.Yu. Sternin, E. Schrohe, “Index problem for elliptic operators associated with a diffeomorphism of a manifold and uniformization”, Dokl. Math., 84:3 (2011), 846-849 (cited: 2) (cited: 2) (cited: 3)
2010
36.
A. Yu. Savin, B. Yu. Sternin, “On the index of noncommutative elliptic operators over $C^*$-algebras”, Sb. Math., 201:3 (2010), 377–417
37.
A. Yu. Savin, B. Yu. Sternin, “Noncommutative elliptic theory. Examples”, Proc. Steklov Inst. Math., 271 (2010), 193–211 (cited: 2) (cited: 2) (cited: 2) (cited: 4)
A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators for the group of dilations”, Dokl. Math., 82:1 (2010), 519-522 (cited: 2) (cited: 1) (cited: 2)
41.
A. Yu. Savin, “On the index of elliptic operators associated with a diffeomorphism of a manifold”, Dokl. Math., 82:3 (2010), 884-886 (cited: 2) (cited: 2) (cited: 3)
42.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “On the Poincaré isomorphism in $K$-theory on manifolds with edges”, Journal of Mathematical Sciences, 170:2 (2010), 238–250
43.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Atiyah–Bott index on stratified manifolds”, Journal of Mathematical Sciences, 170:2 (2010), 229–237
2009
44.
A.Yu. Savin, B.Yu. Sternin, “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521-524
45.
A.Yu. Savin, B.Yu. Sternin, “The index of nonlocal elliptic operators over $C^*$-algebras”, Dokl. Math., 79:3 (2009), 369-372 (cited: 1)
2010
46.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, Journal of Mathematical Sciences, 164:4 (2010), 603–636 (cited: 1) (cited: 1)
2008
47.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “Elliptic theory on manifolds with corners. I: Dual manifolds and pseudodifferential operators”, $C^*$-algebras and Elliptic theory II, Trends in Mathematics, eds. Burghelea, Dan (ed.) et al., Birkhäuser, Basel, 2008, 183-206 (cited: 3)
48.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “Elliptic theory on manifolds with corners. II: Homotopy classification and $K$-homology”, $C^*$-algebras and Elliptic theory II, Trends in Mathematics, eds. Burghelea, Dan (ed.) et al., Birkhäuser, Basel, 2008, 207-226
49.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators”, Dokl. Math., 77:3 (2008), 441-445 (cited: 1)
50.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, Elliptic theory and noncommutative geometry. Nonlocal elliptic operators, Birkhäuser, Basel, 2008 , 224 pp.
2007
51.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192 (cited: 2) (cited: 1) (cited: 1) (cited: 3)
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “On the homotopy classification of elliptic operators on manifolds with corners”, Dokl. Math., 75:2 (2007), 186-189 (cited: 2)
2006
55.
A. Savin, B. Sternin, “Pseudodifferential subspaces and their applications in elliptic theory”, $C^*$-algebras and elliptic theory, Trends in Mathematics, eds. Bojarski, Bogdan (ed.) et al., Birkhäuser, Basel, 2006, 247-289 (cited: 2)
56.
V.E. Nazaikinskii, A.Yu. Savin, B.-W. Schulze, B.Yu. Sternin, Elliptic theory on singular manifolds, Chapman & Hall/CRC, Boca Raton, FL, 2006 , 356 pp.
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Sb. Math., 196:9 (2005), 1271–1305 (cited: 1) (cited: 6) (cited: 6) (cited: 1)
59.
A. Savin, B. Sternin, “Boundary value problems on manifolds with fibered boundary”, Math. Nachr., 278:11 (2005), 1297-1317 (cited: 3) (cited: 3) (cited: 4)
60.
V.E. Nazaikinskii, G. Rozenblum, A.Yu. Savin, B.Yu. Sternin, “Guillemin transform and Toeplitz representations for operators on singular manifolds”, Spectral geometry of manifolds with boundary and decomposition of manifolds., Proceedings of the workshop, Roskilde, Denmark, August 6–9, 2003., Contemporary Mathematics, 366, eds. Booß-Bavnbek, Bernhelm (ed.) et al., AMS, Providence, RI, 2005, 281-306 (cited: 1)
61.
A. Savin, “Elliptic operators on manifolds with singularities and $K$-homology”, K-Theory, 34:1 (2005), 71-98 (cited: 13) (cited: 10) (cited: 13)
62.
V.E. Nazaikinskii, A.Yu. Savin, B.-W. Schulze, B.Yu. Sternin, “The index problem on manifolds with edges”, Noncommutative geometry and representation theory in mathematical physics, Satellite conference to the fourth European congress of mathematics (July 5–10, 2004, Karlstad, Sweden), Contemporary Mathematics, 391, eds. Fuchs, Jürgen (ed.) et al., AMS, Providence, RI, 2005, 289-312 (cited: 1)
63.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, B.-W. Schulze, “Pseudodifferential operators on manifolds with singularities and localization”, Dokl. Akad. Nauk, 402:6 (2005), 743-747 (cited: 1)
2004
64.
A. Yu. Savin, B. Yu. Sternin, “Defect of index in the theory of non-local problems and the $\eta$-invariant”, Sb. Math., 195:9 (2004), 1321–1358 (cited: 3) (cited: 4)
65.
A. Savin, B. Sternin, “The eta invariant and parity conditions”, Adv. Math., 182:2 (2004), 173–203 (cited: 1)
66.
A. Savin, B. Sternin, “Index defects in the theory of spectral boundary value problems”, Aspects of boundary problems in analysis and geometry, Operator Theory: Advances and Applications, 151, eds. Gil, Juan (ed.) et al., Birkhäuser, Basel, 2004, 170-238
67.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “On the definition of pseudodifferential operators on manifolds with singularities”, Dokl. Math., 69:1 (2004), 41-44
68.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, B.-W. Schulze, “On the index of differential operators on manifolds with edges”, Dokl. Math., 69:1 (2004), 68-71
69.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, B.-W. Schulze, “On the existence of elliptic problems on manifolds with edges”, Dokl. Math., 69:2 (2004), 231-234 (cited: 1) (cited: 1)
70.
A. Savin, B. Sternin, “Index for a class of nonlocal elliptic operators”, (in Russian), Spectral and evolution problems, Proceedings of the Fourteenth Crimean Autumn Mathematical School-Symposium (KROMSH-2003) (September 18 – 29, 2003, Sevastopol, Laspi), 14, Taurida National V. Vernadsky University, Simferopol, 2004, 34-40
A. Savin, B.-W. Schulze, B. Sternin, “The $\eta$-invariant and elliptic operators in subspaces”, Jean Leray '99 Conference Proceedings, Math. Phys. Stud., 24, Kluwer Acad. Publ.,, Dordrecht, 2003, 373–387
2002
73.
A. Yu. Savin, B. Yu. Sternin, “The Eta-Invariant and Pontryagin Duality in $K$-Theory”, Math. Notes, 71:2 (2002), 245–261 (cited: 4) (cited: 3)
74.
A.Yu. Savin, B.-W. Schulze, B.Yu. Sternin, “Elliptic operators in subspaces and the eta invariant”, K-Theory, 27:3 (2002), 253–272 (cited: 3) (cited: 2)
2001
75.
A. Savin, B.-W. Schulze, B. Sternin, “On the homotopy classification of elliptic boundary value problems”, Partial differential equations and spectral theory (Clausthal, 2000), Oper. Theory Adv. Appl., 126, eds. Demuth, Michael (ed.) et al., Birkhäuser, 2001, 299–305
76.
A.Yu. Savin, B. Yu. Sternin, “The eta-invariant and parity conditions”, Dokl. Math., 63:2 (2001), 189-193 (cited: 1) (cited: 1)
77.
A.Yu.Savin, B.Yu. Sternin, “On the problem of the homotopy classification of elliptic boundary value problems”, Dokl. Math., 63:2 (2001), 174-178 (cited: 2) (cited: 2)
2000
78.
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213 (cited: 3) (cited: 2)
79.
A. Yu. Savin, B. Yu. Sternin, “Subspaces defined by pseudodifferential projections, and some of their applications”, Dokl. Math., 61:2 (2000), 235-238
80.
A. Yu. Savin, Elliptic operators in subspaces and their applications, Dissertation for Cand. of Phys.-Math. Sciences (PhD), Moscow State University, Moscow, 2000
1999
81.
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in even subspaces”, Sb. Math., 190:8 (1999), 1195–1228 (cited: 8) (cited: 6)
82.
A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On invariant index formulas for spectral boundary value problems”, Differ. Equ., 35:5 (1999), 709–718
83.
A. Yu. Savin, “On operators that allow the decomposition of index formulas for spectral boundary value problems”, Dokl. Math., 60:2 (1999), 220-222
84.
A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, Differ. Uravn., 35:5 (1999), 705–714
1997
85.
A. Yu. Savin, “Branching of terms for the one-dimensional Schrödinger equation”, Differ. Equ., 33:8 (1997), 1055–1062
86.
A. Yu. Savin, Differ. Uravn., 33:8 (1997), 1049–1056
Presentations in Math-Net.Ru
1.
О гомотопической классификации нелокальных эллиптических операторов на многообразиях с цилиндрическими концами А. Ю. Савин International Scientific Conference KOLMOGOROV READINGS – IX. General Control Problems and their Applications (GCP–2020), dedicated to the 70-th birth anniversary of Alexander Ivanovich Bulgakov and to the 90-th anniversary of the Institute of Mathematics, Physics and Information
Technologies of Derzhavin Tambov State University October 12, 2020 16:25
2020
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