Online mini-course "Inequalities, Probabilities and Sobolev Spaces" by Professor of the Faculty of Mathematics Alexander Kolesnikov
As part of the research seminar "Stochastic Analysis with Applications in Economics", from October 5 to November 9, an online mini-course "Inequalities, Probabilities and Sobolev Spaces" by Professor of the Faculty of Mathematics Alexander Kolesnikov is being held.
1. Euclidean isoperimetric inequality and Brunn-Minkowski inequality. Various methods of proof. Transport method. The Sudakov-Tsirelson inequality.
2. The Monge-Kantorovich problem and optimal transportation. Minkowski's problem. Sobolev spaces, classical Sobolev inequalities.
3. The method of semigroups. Gaussian measures and classical Gaussian inequalities (logarithmic Sobolev inequality). Gaussian concentration.
4. Gamma calculus. Logarithmically concave measures. Inequalities of concentration. Connection with isoperimetric problems.
5. Open problems of convex analysis and recent achievements. Stochastic localization method.
6. Other related problems (information inequalities, analysis on manifolds, variants of the Minkowski problem).
It is also worth noting the speech of the invited speaker Vipin Kumar (Institute of Dynamics of Complex Technical Systems named after Max Planck) with the report "Qualitative properties of dynamic equations on time scales".
During the report, the basics of the theory of time scales, dynamical systems on time scales and their properties, the Hilger derivative were discussed. The problems of the initial value in time scales and the change of the parameter formula were considered, as well as the issues of the existence of a unique solution, stability and controllability of the results for pulsed dynamical systems on time scales.