Effects due to gravity and curved space in statistical and quantum models

Abstract

The subject of our research is equations of state and phase diagrams of matter, phase transitions, the role of topology and geometry of space in the evolution of systems, and the effects of the mutual influence of matter and space-time. In this talk we are focusing on 7 problems (5 with Prof. Gavrilik, and indexed by (year)) in areas 2-4 from the list of our interests: 1. strong interacting matter (nuclear, quark-gluon and partonic systems) 2. models on manifolds (Riemann surfaces, homogeneous spaces, Teichmüller space, complements of links and knots) 3. gravitating systems (extremal black holes, Chern-Simons gravity, general relativity) 4. dark matter models (µ-deformed bosons, Bose-Einstein condensate DM with two-phase structure and two-particle composites)