The Chair of Higher Algebra and Geometry

Head of the Chair - Professor B.N. Khabibullin, Doctor of Physics and Mathematics
 
Chair’s history in brief:
The Chair was established in 1957.
Heads of the Chair:
1957-1963 – Associate Professor A.K. Khashaev, Candidate of Physics and Mathematics,
1963-1973 – Associate Professor I.V. Frolova, Candidate of Physics and Mathematics,
1973-1982 - Associate Professor S.B. Ablyalimov, Candidate of Physics and Mathematics,
1982-1995 - Professor S.I. Pinchuk, Doctor of Physics and Mathematics,
Since 1995 the Chair has been headed by Prof. B.N. Khabibullin, Doctor of Physics and Mathematics.
In the 1970-s V.G. Drinfeld, a Fields prize winner was one of the teachers of our Chair.
 
Teaching Work
The Chair’s teaching work is fulfilled at the Faculties of Mathematics and Information Technology, Physics, Biology, Psychology and it also involves gifted schoolchildren. It is performed by 1 professor, 6 associate professors, 1 assistant lecturer, and 1 senior lecturer (honored teacher of Bashkortostan).
Main Courses:
  • Analytical Geometry (Faculties of Mathematics and Information Technology and Physics),
  • Higher Algebra (Faculty of Physics),
  • Algebra,
  • Number Theory,
  • Multidimensional Geometry and Linear Algebra,
  • Differential Geometry,
  • Vector and Tensor Analysis (Faculty of Physics),
  • Basic Geometry and History of Mathematics,
  • Methods of Teaching Mathematics,
  • Additional Course on Geometry and Topology,
  • Topology,
  • History and Methods of Mathematics (for undergraduates),
  • History and Methods of Information Science (for undergraduates),
  • Contemporary Problems of Mathematics and Information Science (for undergraduates),
  • Higher Mathematics (Faculties of Biology and Psychology)
 
Main Research Areas
  • Differential geometry (spline curves and curve approximation, spinors)
  • Complex analysis (entire functions, potential theory, pluri– and subharmonic functions)
  • Distribution of zeroes in holomorphic functions
  • Function system completeness
  • Closed ideals and submodules in function classes
  • Spectral synthesis
  • Geometric theory and CR-functions
  • Separate algebraicity in algebraic curve series
  • Ordered vector spaces (vector lattices, vector lattice projection limits, dual type functionals, sublinear functionals)
  • Dynamic systems (integrated systems, systems with normal shift)
  • Differential equations (classification of nonlinear integrated hyperbolic systems and algebraic analogues of the Painlevé equations, the problem of point equivalence and group DE Analysis)
  • Nonlinear plasticity theory (including continual limit dislocation theory)
  • Methods of teaching mathematics (test and control theory, the Rasch model, scaling and validity)
  • Spectral theory (the Schrödinger operator in a magnetic field)
  • Structural group theory (transfinite normal and composition series, transfinite supersimplicity)
  • Elementary particle theory (the Standard model and its variants, the Higgs boson problem).
 
         Grants, Projects, Conferences, Seminars
 
         The Chair has been conducting research in more than 30 grant projects of the Russian Fundamental Research Fund, Federal Innovation Agency, RF President Fund, INTAS etc. The grants got made it possible to set up annual conferences (regional conferences in 2001-2004, 2006, 2008, international conferences in 2005, 2009, all-Russian conferences in 2006, 2007) for students, postgraduates, and young scientists, which result in publishing both articles and full-volume studies (up to 10 volumes).
Scientific Links

The Chair has established links with Universities of Kazan, Novgorod, Novosibirsk, Moscow, St. Petersburg, Rostov, mathematical institutes of the Academy of Sciences, leading universities and institutes of Bulgaria, Germany, Greece, Great Britain, Israel, India, Spain, Italy, Kazakhstan, Canada, Cyprus, China, Malta, Mongolia, Norway, Chile, the USA, Turkey, Ukraine, France, and Sweden.