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. V. Boltachev, A. Yu. Savin, “Trajectory symbols and the Fredholm property of boundary value problems for differential operators with shifts”, Russ. J. Math. Phys., 30:2 (2023), 135–151
A. Savin, E. Schrohe, “Trace expansions and equivariant traces on an algebra of Fourier integral operators on Rn”, Cyclic cohomology at 40: achievements and future prospects, Proc. Sympos. Pure Math., 105, AMS, 2023, 457–476
K. N. Zhuikov, A. Yu. Savin, “Eta-invariant of elliptic parameter-dependent boundary-value problems”, CMFD, 69, no. 4, PFUR, M., 2023, 599–620
2022
7.
A. Baldare, V. E. Nazaikinskii, A. Yu. Savin, E. Schrohe, “$C^*$-Algebras of Transmission Problems and Elliptic Boundary Value Problems with Shift Operators”, Math. Notes, 111:5 (2022), 701–721
8.
K. N. Zhuikov, A. Yu. Savin, “Eta-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group”, Math. Notes, 112:5 (2022), 685–696
9.
K. N. Zhuikov, A. Yu. Savin, “Eta-invariant for parameter-dependent families with periodic coefficients”, Ufa Math. J., 14:2 (2022), 35–55
10.
N. R. Izvarina, A. Yu. Savin, “An Atiyah-Bott-Lefschetz theorem for relative elliptic complexes”, Lobachevskii J. Math., 43:10 (2022), 2675–2684
11.
A. V. Boltachev, A. Yu. Savin, “Index of twisted elliptic boundary value problems associated with isometric group actions”, Lobachevskii J. Math., 43:10 (2022), 2635–2646
12.
V. E. Nazaikinskii, A. Yu. Savin, “On semiclassical asymptotics for nonlocal equations”, Russ. J. Math. Phys., 29:4 (2022), 568–575
13.
A. V. Boltachev, A. Yu. Savin, “Periodic cyclic cocycles on the Boutet de Monvel symbol algebra”, Russ. J. Math. Phys., 29:4 (2022), 417–425
14.
A. Savin, E. Schrohe, “Local index formulae on noncommutative orbifolds and equivariant zeta functions for the affine metaplectic group”, Adv. Math., 409, Part A (2022), 108624 , 37 pp.
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.
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
20.
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
21.
A. Savin, E. Schrohe, B. Sternin, “Elliptic operators associated with groups of quantized canonical transformations”, Bull. Sci. Math., 155 (2019), 141–167
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
23.
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
24.
A. Savin, B. Sternin, Introduction to complex theory of differential equations, Birkhäuser, Basel, 2017 , 1-128 pp.
A.Yu. Savin, B.Yu. Sternin, “Elliptic differential dilation-contraction problems on manifolds with boundary”, Differ. Equ., 53:5 (2017), 665–676
2018
26.
A. Yu. Savin, B. Yu. Sternin, “Elliptic G-Operators on Manifolds with Isolated Singularities”, Journal of Mathematical Sciences, 233 (2018), 930–948
2016
27.
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
28.
A. Yu. Savin, B. Yu. Sternin, “Ellipticheskie zadachi s rastyazheniyami-szhatiyami na mnogoobraziyakh s kraem”, Doklady akademii nauk, 469:2 (2016), 154–156
29.
A.Yu. Savin, B.Yu. Sternin, “Elliptic dilation-contraction problems on manifolds with boundary. C*-theory”, Differ. Equ., 52:10 (2016), 1331–1340
30.
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
31.
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
32.
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
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
34.
A. Yu. Savin, B. Yu. Sternin, “Index of Sobolev problems on manifolds with many-dimensional singularities”, Differ. Equations, 50:2 (2014), 232–245
35.
A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Doklady Mathematics, 89:1 (2014), 61-64
36.
A.Yu. Savin, B. Yu. Sternin, “Index of nonlocal problems associated with a bundle”, Differ. Equations, 50:8 (2014), 1112–1121
37.
A. Yu. Savin, B.Yu. Sternin, “Index of elliptic operators for diffeomorphisms of manifolds”, J. of Noncommutative Geometry, 8:3 (2014), 695–734
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
A. Yu. Savin, B. Yu. Sternin, “Uniformization of nonlocal elliptic operators and KK-theory”, Russian Journal of Mathematical Physics, 20:3 (2013), 345–359
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
44.
A. Yu. Savin, B.Yu. Sternin, “Elliptic translators on manifolds with point singularities”, Differ. Equations, 48:12 (2012), 1577–1585
2011
45.
A.Yu. Savin, B.Yu. Sternin, “On the index of elliptic translators”, Dokl. Math., 83:1 (2011), 76-79
A. Yu. Savin, B. Yu. Sternin, “On the index of elliptic operators for the group of dilations”, Sb. Math., 202:10 (2011), 1505–1536
48.
A. Yu. Savin, “On the symbol of nonlocal operators in Sobolev spaces”, Differ. Equ., 47:6 (2011), 897–900
49.
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
50.
A. Yu. Savin, “On the Index of Nonlocal Elliptic Operators Corresponding to a Nonisometric Diffeomorphism”, Math. Notes, 90:5 (2011), 701–714
51.
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
2010
52.
A. Yu. Savin, B. Yu. Sternin, “On the index of noncommutative elliptic operators over $C^*$-algebras”, Sb. Math., 201:3 (2010), 377–417
53.
A. Yu. Savin, B. Yu. Sternin, “Noncommutative elliptic theory. Examples”, Proc. Steklov Inst. Math., 271 (2010), 193–211
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
59.
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
60.
A.Yu. Savin, B.Yu. Sternin, “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521-524
61.
A.Yu. Savin, B.Yu. Sternin, “The index of nonlocal elliptic operators over $C^*$-algebras”, Dokl. Math., 79:3 (2009), 369-372
2010
62.
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
2008
63.
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
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
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192
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
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
75.
A. Savin, B. Sternin, “Boundary value problems on manifolds with fibered boundary”, Math. Nachr., 278:11 (2005), 1297-1317
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
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
79.
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
2004
80.
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
81.
A. Savin, B. Sternin, “The eta invariant and parity conditions”, Adv. Math., 182:2 (2004), 173–203
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
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
84.
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
85.
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
86.
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
89.
A. Yu. Savin, B. Yu. Sternin, “The Eta-Invariant and Pontryagin Duality in $K$-Theory”, Math. Notes, 71:2 (2002), 245–261
90.
A.Yu. Savin, B.-W. Schulze, B.Yu. Sternin, “Elliptic operators in subspaces and the eta invariant”, K-Theory, 27:3 (2002), 253–272
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
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213
95.
A. Yu. Savin, B. Yu. Sternin, “Subspaces defined by pseudodifferential projections, and some of their applications”, Dokl. Math., 61:2 (2000), 235-238
96.
A. Yu. Savin, Elliptic operators in subspaces and their applications, Dissertation for Cand. of Phys.-Math. Sciences (PhD), Moscow State University, Moscow, 2000
1999
97.
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in even subspaces”, Sb. Math., 190:8 (1999), 1195–1228
98.
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
99.
A. Yu. Savin, “On operators that allow the decomposition of index formulas for spectral boundary value problems”, Dokl. Math., 60:2 (1999), 220-222
100.
A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, Differ. Uravn., 35:5 (1999), 705–714
1997
101.
A. Yu. Savin, “Branching of terms for the one-dimensional Schrödinger equation”, Differ. Equ., 33:8 (1997), 1055–1062
102.
A. Yu. Savin, Differ. Uravn., 33:8 (1997), 1049–1056
$\eta$-invariants of elliptic boundary value problems A. Yu. Savin VI International Conference "Function Spaces. Differential Operators. Problems of Mathematical Education", dedicated to the centennial anniversary of the corresponding member of Russian Academy of Sciences, academician of European Academy of Sciences L.D. Kudryavtsev November 17, 2023 16:35
5.
Eta-invariants for families of operators with shifts A. Yu. Savin, K. N. Zhuikov III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov July 12, 2023 12:35
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