• Algebraic Topology
  • Combinatorial Topology
  • Low-dimensional Topology and Knot Theory
  • Topology of Manifolds
  • Toric Topology
  (researchers: Sergey Novikov, Levan Alania, Ivan Babenko, Victor Buchstaber, Alexey Chernavskii, Alexander Gaifullin, Dmitriy Gugnin, Ivan Dynnikov, Nickolay Erochovets, Dmitri Millionshchikov, Alexander Mishchenko, Taras Panov, Alexander Zarelua)

• Noncommutative Geometry
  (researchers: Alexander Mishchenko, Vladimir Manuilov, Evgeniy Troitsky)

• Integrable Systems
  (researchers: Sergey Novikov, Victor Buchstaber, Boris Dubrovin, Ivan Dynnikov, Piotr Grinevich, Oleg Mokhov, Alexei Penskoi, Sergey Smirnov, Dmitri Talalaev, Alexander Veselov)

• Differential Geometry
  (researchers: Oleg Mokhov, Alexey Penskoi)

• Singularity Theory
  (researcher: Sabir Gusein-Zade)

• Discrete and Combinatorial Geometry
  (researchers: Victor Buchstaber, Nickolay Erochovets, Alexander Gaifullin, Alexey Garber, Taras Panov)

The work of the members of our department has been widely recognised by the world scientific community. Sergey Novikov was awarded the Fields Medal of the International Mathematical Union, the highest international award for research in mathematics. Victor Buchstaber, Alexander Mishchenko and Sergey Novikov were invited speakers at the International Mathematical Congresses. Ivan Dynnikov and Alexander Gaifullin delivered invited talks at the European Congresses of Mathematicians. The scientific work of Sergey Novikov was awarded the USSR Lenin Prize. Alexander Mishchenko was awarded the State Prize of the Russian Federation.

Department staff gave numerous invited presentations at international scientific conferences and maintain active contacts with leading foreign scientists and research centers. The scientific schools of Sergey Novikov, Victor Buchstaber and Alexander Mishchenko have become world-famous.