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Laboratory of Algebraic Geometry and its Applications

Invited researcher Fyodor Alexeyevich Bogomolov
Contract number
11.G34.31.0023
Time span of the project
2010-2014

As of 18.05.2020

42
Number of staff members
293
scientific publications
General information

Name of the project: Algebraic geometry and its applications

Strategy for Scientific and Technological Development Priority Level: а


Goals and objectives

Research directions: Research in algebraic geometry and adjacent domains: homological algebra, number theory, differential and complex geometry, and geometrical analysis

The practical value of the study

  • We have proven the global Torelli theorem for hyperkahler manifolds.
  • A cathegorical resolution of arbitrary algebraic singularities has been built.
  • We have proven homological mirror symmetry for complex algebraic curves.
  • Our researchers have proven smoothness of the manifold of moduli of mathematical instantons.

Implemented results of research: Scientific research of the Laboratory are devoted to development of ideas and methods of fundamental mathematics. New scientific results produced over the course of implementation of the project are, in particular, used in tutoring of mathematical disciplines at the Higher School of Economics.

Education and career development:

  • 3 doctoral dissertations and 11 candidate dissertations have been defended.
  • Members of the academic staff of the Laboratory regularly read special courses and run scientific workshops that are included into the pool of elective courses of the faculty, as well as courses at the Science and Education Center of the Steklov Mathematical Institute of Russian Academy of Sciences and the Independent University of Moscow.
  • We are regularly conducting schools for students, postgraduates, and young scientists entitled «Algebra and geometry» on the basis of the Yaroslavl State Pedagogical University named after K. D. Ushinskiy that also features an additional training program.

Organizational and structural changes: On the grounds of the Laboratory and the Faculty of Mathematics we have related a computer appliances complex for conducting research and computations in fundamental mathematics and related domains. The complex incorporates a range of software, both free and proprietary.

Other results: Over the period between 2010 and 2018,four members of the academic staff of the Laboratory have become invited speakers at International Mathematical Congresses (2010 – the 26t in Hyderabad, India; 2014 – the 27th, Seoul, South Korea; 2018 – the 28th in Rio de Janeiro, Brazil).

Collaborations:

  • Courant Institute of Mathematical Sciences of New York University (USA): joint research in special manifolds, scientific publications
  • University of Edinburgh (United Kingdom): joint scientific research in classical geometry, scientific publications, participation in academic events conducted by the Laboratory
  • European Center for Scientific Research in Mathematics and Physics (France): joint research in special manifolds and homological and motivic methods in non-commutative geometry, scientific publications, participation of researchers in scientific events conducted by the Laboratory, student exchange


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Kuznetsov A.G., Lunts V.
Categorical Resolutions of Irrational Singularities. International Mathematics Research Notices 2015(13): 4536–4625 (2015).
Verbitsky M.
Mapping Class Group and a Global Torelli Theorem for Hyperkahler Manifolds. Duke Mathematical Journal 162(15): 2929–2986 (2013).
Kaledin D.
Witt Vectors as a Polynomial Functor. Selecta Mathematica 24(1): 359–402 (2018).
Amerik E., Bogomolov F., Rovinsky M.
Remarks on Endomorphisms and Rational Points. Compositio Mathematica 147(6): 1819–1842 (2011).
Mori S., Prokhorov Y.
Threefold Extremal Contractions of Type IA. Journal of Mathematics of Kyoto University 51(2): 393–438 (2011).
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