Computational and applied topology

The group of Roman Karasev, D.Sc.

The group also includes:

• A. Akopyan, Ph.D.;
• S. Melikhov, Ph.D.;
• A. Nikitenko;
• D. Tonkonog;
• E. Shchepin, D.Sc., corresponding member of Russian Academy of Sciences;
• V. Volkov;
• A. Volovikov, Ph.D.

We develop topological methods in computational geometry, in particular, for image recognition and high dimensional data analysis, based on the use of persistence diagrams. The algebraic foundations of the persistent homology are also studied. We also apply topological methods to different problems in discrete geometry connected to measure partitions and similar questions.