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Depart ment of Mathematical Physics

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Scientific Interests
Experience
Conferences
Publications

About the Department

Yury Arkadievich Kordyukov

Leading Researcher,
Doctor of Science

ykordyukov@yahoo.com

Scientific Interests

  • Analysis on manifolds, in particular, on foliated manifolds

  • Spectral theory and index theory of pseudodifferential operators

  • Noncommutative differential geometry

Experience

  • 1984 Mathematician diploma, Moscow State University
  • 1984 - 1987 post-graduate in Department of Mathematics of MSU
  • 1988 PhD, Moscow Institute of Electronic Engineering, thesis "Elliptic operators on manifolds with limited geometry"
  • Since 1988 work in Ufa State Aviation Technical University, since 1995 docent of Chair of Mathematics
  • 2002 - current work in Institute of Mathematics of USC RAS, leading researcher (2005)
  • 2004 Doctor's degree, thesis "Analysis of differential operators on foliated manifolds", Institute of Mathematics of USC RAS

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Conferences

  • June 2005, Foliations 2005, Lodz, Poland.
  • February 2005 Topology, Analysis and Applications to Mathematical Physics, Moscow.
  • September 2004 XV Crimean Autumn Mathematical School-Symposium, Ukraine.
  • February 2004 $C^*$-algebras and elliptic theory, Banach Center, Bedlewo, Poland.
  • September 2003 XIV Crimean Autumn Mathematical School-Symposium, Ukraine.
  • August 2003 Noncommutative Geometry and Number Theory, Bonn, Germany.
  • August 2003 Curvature and Global Shape, Munster, Germany.
  • June 2003 Kolmogorov and contemporary mathematics, Moscow, Russia.
  • August 2002 Noncommutative geometry and fractional quantum Hall effect, Adelaide, Australia.
  • June 2002 Second Russian-German Meeting dedicated to 90-anniversary of A.D. Alexandrov, St. Petersburg, Russia.
  • October 2000 Modern group analysis for the new millennium, Ufa, Russia.
  • September 2000 Trends in noncommutative algebra and geometry, Bonn, Germany.
  • May 2000 Complex Analysis, Differential Equations and Related Topics, Ufa, Russia.
  • March 2000 Geometry and Applications, Novosibirsk, Russia.
  • August 1999 $L^2$-invariants and K-theory, Munster, Germany.
  • 1998 Spectral theory of differential operators and related problems, Sterlitamak, Russia.
  • March 1998 Special Topology Program, Tel-Aviv, Israel.
  • June 1996 Geometrische Analysis auf singularen Raumen, Oberwolfach, Germany.
  • July 1994 VII International Colloquium on Differential Geometry, Santiago de Compostela, Spain.
  • January 1994 International Conference "Differential Equations and its Applications" dedicated to Petrovski, Moscow, Russia.
  • January 1994 Voronezh Winter Mathematical School, Russia.
  • May 1993 Pontryaginskie chteniya-IV, Voronezh, Russia.
  • November 1992 Global Analysis, Usedom, Germany.
  • June 1991 Modern Group Analysis, Ufa, Russia.
  • September 1990 XVI School on theory of operators in function spaces, Ulyanovsk, Russia.
  • January 1990 Voronezh All-Union Winter Mathematical School, Russia.
  • September 1989 XV School on theory of operators in function spaces, Novgorod, Russia.

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Publications

  • Kordyukov Yu. A. Noncommutative geometry of foliations, preprint math.DG/0504095, 105 pp.
  • Kordyukov Yu. A. Egorov's theorem for transversally elliptic operators on foliated manifolds and noncommutative geodesic flow. Math. Phys. Anal. Geom. 8 (2005), 97-119.
  • Kordyukov Yu. A., V. Mathai and M. Shubin. Equivalence of projections in semiclassical limit and a vanishing theorem for higher traces in $K$-theory. J. Reine Angew. Math. 581(2005), 193-236.
  • Kordyukov Yu. A. Spectral gaps for periodic Schr\"odinger operators with strong magnetic fields. Commun. Math. Phys. 253(2005), 371-384.
  • Kordyukov Yu. A. Semiclassical spectral asymptotics on foliated manifolds. Math. Nachr. 245(2002), 104 - 128.
  • J. \'Alvarez L\'opez, Kordyukov Yu. A. Distributional Betti numbers of transitive foliations of codimension one. In: Foliations: Geometry and Dynamics. Proceedings of Euroworkshop held in Warsaw, Poland 29 May - 9 June 2000. - Singapore: World Scientific, 2002, pp. 159-183.
  • J. \'Alvarez L\'opez, Kordyukov Yu. A. Long time behavior of leafwise heat flow for Riemannian foliations. Compositio Math. 125(2001), 129-153.
  • J. \'Alvarez L\'opez, Kordyukov Yu. A. Adiabatic limits and spectral sequences for Riemannian foliations. Geom. and Funct. Anal. 10(2000), 977-1027.
  • Kordyukov Yu. A. The trace formula for transversally elliptic operators on Riemannian foliations (Russian). Algebra i Analiz 12(2000), no.3, 81-105; translation in St. Petersburg Math. J. 12(2001), no. 3, 407-422.
  • Kordyukov Yu. A. $L^{p}$-estimates for functions of elliptic operators on manifolds of bounded geometry. Russian J. Math. Phys. 7(2000), no. 2, 216-229.
  • Kordyukov Yu. A. Adiabatic limits and spectral geometry of foliations. Math. Ann. 313(1999), 763-783.
  • Kordyukov Yu. A. Noncommutative spectral geometry of Riemannian foliations. Manuscripta Math. 94(1997), 45-73.
  • Kordyukov Yu. A. Functional calculus for tangentially elliptic operators on foliated manifolds. In: Analysis and Geometry in Foliated Manifolds, Proceedings of the VII International Colloquium on Differential Geometry, Santiago de Compostela, 1994. - Singapore: World Scientific, 1995, pp. 113-136.
  • Kordyukov Yu. A. Semiclassical asymptotics of spectra of hypoelliptic operators on foliated manifold (Russian). Funktsional. Anal. i Prilozhen. 29(1995), no. 3, 80-82; translation in Funct. Anal. Appl. 29(1995), no. 3, 211-213.
  • Kordyukov Yu. A. Transversally elliptic operators on $G$-manifolds of bounded geometry (contunued). Russian J. Math. Phys. 3(1995), no. 1, 41-64.
  • Kordyukov Yu. A. Transversally elliptic operators on $G$-manifolds of bounded geometry. Russian J. Math. Phys. 2(1994), no. 2, 175-198.
  • Kordyukov Yu. A. On semiclassical asymptotics of spectra of elliptic operators on foliated manifold (Russian). Mat. Zametki 53(1993), no. 1, 157-159; translation in Mathem. Notes 53(1993), no. 1-2, 104-105.
  • Kordyukov Yu. A. $L^{p}$-theory of elliptic differential operators on manifolds of bounded geometry. Acta Appl. Math. 23(1991), 223-260.
  • Kordyukov Yu. A. $L^{p}$-theory of elliptic differential operators with bounded coefficients (Russian). Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1988, no. 4, 98-100; translation in Moscow Univ. Math. Bull. 43 (1988), no. 4, 103-106.
  • Kordyukov Yu. A. $L^{p}$- theory of elliptic differential operators with bounded coefficients (Russian). Preprint VINITI no. 6005-B87, 1987, 46pp.
  • Kordyukov Yu. A. Spectral theory of tangentially elliptic operators on foliated manifolds (Russian). Preprint VINITI no. 7288-B87, 1987, 35pp.
  • Kordyukov Yu. A. A theorem on the identity of spectra for tangentially elliptic operators on foliated manifolds (Russian). Funktsional. Anal. i Prilozhen. 19(1985), no. 4, 90-91; translation in Funct. Anal. Appl. 19 (1985), no. 4, 327-328.

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Yu.A. Kordyukov