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
V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192
6.
A. Yu. Savin, B. Yu. Sternin, “Elliptic operators in odd subspaces”, Sb. Math., 191:8 (2000), 1191–1213
7.
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.
A. Savin, E. Schrohe, B. Sternin, “Elliptic operators associated with groups of quantized canonical transformations”, Bull. Sci. Math., 155 (2019), 141–167
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. Yu. Savin, B. Yu. Sternin, “On the index of elliptic operators for the group of dilations”, Sb. Math., 202:10 (2011), 1505–1536
11.
A. Yu. Savin, B. Yu. Sternin, “Noncommutative elliptic theory. Examples”, Proc. Steklov Inst. Math., 271 (2010), 193–211
12.
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
13.
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.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
K. N. Zhuikov, A. Yu. Savin, “Eta-invariant for parameter-dependent families with periodic coefficients”, Ufa Math. J., 14:2 (2022), 35–55
23.
A.Yu. Savin, B.Yu. Sternin, “Elliptic dilation-contraction problems on manifolds with boundary. C*-theory”, Differ. Equ., 52:10 (2016), 1331–1340
24.
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
25.
A. Yu. Savin, B. Yu. Sternin, “The Eta-Invariant and Pontryagin Duality in $K$-Theory”, Math. Notes, 71:2 (2002), 245–261
26.
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
27.
A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, Differ. Uravn., 35:5 (1999), 705–714
28.
A. Yu. Savin, E. N. Semenova, “A spectral Sobolev problem for the biharmonic operator”, Lobachevskii J. Math., 44:3 (2023), 950–955
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
30.
A.Yu. Savin, B.Yu. Sternin, “Elliptic differential dilation-contraction problems on manifolds with boundary”, Differ. Equ., 53:5 (2017), 665–676
A. Yu. Savin, B. Yu. Sternin, “On the index of noncommutative elliptic operators over $C^*$-algebras”, Sb. Math., 201:3 (2010), 377–417
34.
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
35.
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
K. N. Zhuikov, A. Yu. Savin, “Eta-invariant of elliptic parameter-dependent boundary-value problems”, CMFD, 69, no. 4, PFUR, M., 2023, 599–620
39.
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
40.
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. Yu. Savin, B. Yu. Sternin, “Elliptic G-Operators on Manifolds with Isolated Singularities”, Journal of Mathematical Sciences, 233 (2018), 930–948
44.
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
45.
A. Yu. Savin, B.Yu. Sternin, “Elliptic translators on manifolds with multidimensional singularities”, Differ. Equations, 49:4 (2013), 494–509
46.
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
47.
A. Yu. Savin, B.Yu. Sternin, “Elliptic translators on manifolds with point singularities”, Differ. Equations, 48:12 (2012), 1577–1585
48.
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, 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
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-Invariants for Parameter-Dependent Operators Associated with an Action of a Discrete Group”, Math. Notes, 112:5 (2022), 685–696
55.
N. R. Izvarina, A. Yu. Savin, “An Atiyah-Bott-Lefschetz theorem for relative elliptic complexes”, Lobachevskii J. Math., 43:10 (2022), 2675–2684
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
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
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
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. 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
69.
V. E. Nazaikinskii, A. Yu. Savin, “On semiclassical asymptotics for nonlocal equations”, Russ. J. Math. Phys., 29:4 (2022), 568–575
70.
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
71.
A. Savin, E. Schrohe, “An index formula for groups of isometric linear canonical transformations”, Doc. Math., 27 (2022), 983–1013
72.
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
73.
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
74.
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
75.
A. Yu. Savin, B. Yu. Sternin, “Ellipticheskie zadachi s rastyazheniyami-szhatiyami na mnogoobraziyakh s kraem”, Doklady akademii nauk, 469:2 (2016), 154–156
76.
Anton Savin, Elmar Schrohe, Boris Sternin, Elliptic Operators Associated with Groups of Quantized Canonical Transformations, 2016 (Published online) , 23 pp., arXiv: arXiv:1612.02981
77.
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
78.
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
79.
A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators associated with fibrations”, Doklady Mathematics, 89:1 (2014), 61-64
80.
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
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
83.
A.Yu. Savin, B.Yu. Sternin, “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521-524
84.
A.Yu. Savin, B.Yu. Sternin, “The index of nonlocal elliptic operators over $C^*$-algebras”, Dokl. Math., 79:3 (2009), 369-372
85.
V.E. Nazaikinskii, A.Yu. Savin, B.Yu. Sternin, “On the index of nonlocal elliptic operators”, Dokl. Math., 77:3 (2008), 441-445
86.
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.
87.
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
88.
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
89.
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
90.
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
91.
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
92.
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
95.
A.Yu. Savin, B. Yu. Sternin, “The eta-invariant and parity conditions”, Dokl. Math., 63:2 (2001), 189-193
96.
A. Yu. Savin, B. Yu. Sternin, “Subspaces defined by pseudodifferential projections, and some of their applications”, Dokl. Math., 61:2 (2000), 235-238
97.
A. Yu. Savin, Elliptic operators in subspaces and their applications, Dissertation for Cand. of Phys.-Math. Sciences (PhD), Moscow State University, Moscow, 2000
98.
A. Yu. Savin, “On operators that allow the decomposition of index formulas for spectral boundary value problems”, Dokl. Math., 60:2 (1999), 220-222
99.
A. Yu. Savin, “Branching of terms for the one-dimensional Schrödinger equation”, Differ. Equ., 33:8 (1997), 1055–1062
100.
A. Yu. Savin, Differ. Uravn., 33:8 (1997), 1049–1056
101.
Math. Notes, 116:2 (2024), 139–167
102.
K. N. Zhuikov, A. Yu. Savin, “On two methods of determining $\eta$-invariants of elliptic boundary-value problems”, CMFD, 70, no. 3, PFUR, M., 2024, 403–416
$\eta$-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
9.
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