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Georgy I. Sharygin

Georgy I. Sharygin

Candidate of Physical and Mathematical Sciences (PhD), Docent

Department of Differential Geometry and Applications
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University
Main Building, 1 Leninskiye Gory, Moscow 119991, GSP-1, Russia

E-mail: sharygin@itep.ru

Full list of publications

1. Life and career

Georgy I. Sharygin was born in 1974 in Moscow. In 1991 he finished Moscow school No. 45 with advanced study of English. From 1991 to 1996 he studied in the full-time stream of the Division of Mathematics of the Faculty of Mechanics and Mathematics of MSU, specialising at the Department of Differential Geometry and Applications under the supervision of Professor Yu. P. Solovyov. His diploma thesis was devoted to Pontryagin characteristic classes of symmetric spaces.

From 1996 to 1999 he studied in the postgraduate programme at the Department of Differential Geometry and Applications (advisor Yu. P. Solovyov). In 2000 he defended his candidate dissertation “Geometry of non-commutative principal bundles”.

From 1999 to 2010 he worked as assistant and then docent at the Department of Mathematics of the SUSC of MSU (the Kolmogorov school), teaching algebra and, above all, elementary geometry to school students; since the autumn of 2010 he has continued there part-time. Since 2001 he has also worked as a researcher at ITEP (Institute for Theoretical and Experimental Physics), and since 2004 as docent at the Department of Elementary Mathematics of Moscow State Pedagogical University (part-time).

2. Degrees and positions

Born1974, Moscow.
EducationFaculty of Mechanics and Mathematics, MSU, 1991–1996; postgraduate programme at the Department of Differential Geometry and Applications 1996–1999.
Candidate of Physical and Mathematical Sciences (PhD)2000; advisor Professor Yu. P. Solovyov. Thesis: “Geometry of non-commutative principal bundles”.
PositionsAssistant and Docent, Department of Mathematics, SUSC of MSU (1999–2010, part-time since 2010); Researcher, ITEP (since 2001); Docent, Department of Elementary Mathematics, MSPU (since 2004, part-time).
Research fieldsNon-commutative geometry; cyclic homology and Hopf-cyclic cohomology; characteristic classes; differential geometry in the large.

3. Research

In studying topological spaces one often draws conclusions about the structure of a space from properties of the algebra of its functions. For instance, de Rham cohomology, one of the main topological invariants of a smooth manifold, depends only on the structure of the algebra of smooth functions (this statement is made precise by cyclic homology). Similar examples occur elsewhere in mathematics: a Poisson structure on a manifold can be formulated as a Lie algebra structure on the algebra of smooth functions, and integrability of a Hamiltonian system can be expressed in the same language.

All these notions are to a large extent algebraic and can be studied with modern algebraic machinery. Most of these methods apply only to commutative algebras, whereas many important non-commutative algebras are naturally associated with topological spaces. The idea behind non-commutative geometry is to obtain useful information by studying non-commutative algebras as if they were algebras of functions on “non-commutative” or “quantum” spaces.

G. I. Sharygin's work develops this programme: Hopf-cyclic cohomology of algebras and coalgebras with coefficients, pairings in Hopf-cyclic cohomology, the structure of Hopf-cyclic (co)homology of algebras of smooth functions, Hopf cyclic cohomology and the Chern character of equivariant K-theories, and the geometry of non-commutative principal bundles.

4. Teaching

For more than a decade G. I. Sharygin taught algebra and elementary geometry at the Kolmogorov school (SUSC of MSU), and since 2004 he has taught at the Department of Elementary Mathematics of Moscow State Pedagogical University.

5. Publications

Full list of publications — 146 records (department page and ISTINA profile)

A PDF version of the departmental list is also available:

G. I. Sharygin — list of publications (PDF)

Selected works:

  1. I. M. Nikonov, G. I. Sharygin. On the Hopf-type cyclic cohomology with coefficients. In: C*-Algebras and Elliptic Theory, Trends in Mathematics, Birkhauser, 2006, pp. 203–212.
  2. I. M. Nikonov, G. I. Sharygin. Pairings in Hopf-cyclic cohomology of algebras and coalgebras with coefficients. Journal of K-Theory, vol. 5, no. 2 (2010), pp. 289–348.
  3. I. M. Nikonov, G. I. Sharygin. Structure of Hopf-cyclic (co)homology of algebras of smooth functions. Mathematical Notes, vol. 97, no. 4 (2015), pp. 566–582.
  4. I. M. Nikonov, G. I. Sharygin. Hopf cyclic cohomology and Chern character of equivariant K-theories. Russian Journal of Mathematical Physics, vol. 22, no. 3 (2015), pp. 379–388.
  5. G. I. Sharygin, A. Yu. Konyaev. Survey of the deformation quantization of commutative families. In: Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, Springer Proceedings in Mathematics & Statistics, 273 (2018).