(in Polish) Nierówności w geometrii wypukłej 1000-1M17NGW
1. Brunn-Minkowski inequality, isoperimetric inequality, Prekopa-Leindler inequality
2. Steiner symmetrization, Urysohn inequaliyu
3. Blashke-Santalo inequality
4. Spherical and Gaussian isoperimetry, Gaussian concentration, Ehrhard inequality
5. Brascamp-Lieb inequality
6. Revers isoperimetric inequality and, John elipsoid theorem
7. Localizaton techniques
8. Khinchine inequalities and sections of balls in l_p^n norms
9. Gaussian correlation
10. Inequalities for Shannon entropy
Type of course
Mode
Prerequisites (description)
Course coordinators
Learning outcomes
1. Student knows and understands basic inequalities in convex geometry.
2. Student knows and is able to use basic proof techniques.
Assessment criteria
Optional: homework problems, midterm exam
Obligatory: oral exam
Homework and midterm problems solved will be an advance toward oral exam (in case of good marks exemption possible).
Bibliography
S. Artstein-Avidan, A. Giannopoulos, and V. D. Milman. Asymptotic geometric analysis. Part I, volume 202 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2015.
P. Nayar, T. Tkocz, Extremal sections and projections of certain convex bodies: a survey, arXiv:2210.00885
R. Latała, D. Matlak, Royen's proof of the Gaussian correlation inequality, arXiv:1512.08776
K. Ball, An Elementary Introduction to Modern Convex Geometry, in Flavors of Geometry (Silvio Levy ed.), MSRI lecture notes, CUP (1997).
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: