1. In mathematical terms, random vibration is characterized as an ergodic and stationary process.

2. Bryna Kra works in ergodic theory and dynamical systems, particularly on problems motivated by combinatorics and number theory.

3. Recently, great progress has been made at the interface of operator algebras, Descriptive Set Theory and Ergodic Theory.

4. Areas of current activity include complex, harmonic, and real Analysis; dynamical systems and ergodic theory; functional Analysis; mathematical physics; operator theory and operator algebras; partial differential equations and …

5. Numerous results have been achieved so far, in particular regarding rigidity results for von Neumann algebras and so-called von Neumann equivalence arising from so-called measure-preserving ergodic a.e. free group actions.

6. As of 2015, IMPA does research in algebra, analysis, differential geometry, partial differential equations, computer graphics, fluid dynamics, holomorphic dynamics, mathematical economics, symplectic geometry, algebraic geometry, optimization, probability theory, dynamical systems, and ergodic theory.

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