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(in Polish) Nierówności w geometrii wypukłej

General data

Course ID:	1000-1M17NGW
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	(unknown)
Name in Polish:	Nierówności w geometrii wypukłej
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	6.00 Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	(unknown)
Type of course:	elective monographs
Prerequisites (description):	Linear algebra, mathematical analysis of one and several variables, probability theory
Mode:	Classroom
Short description:	Convex geometry deals mainly with convex sets in Euclidean spaces. During the lectures we shall focus on certain important inequalities in this field, including isoperimetric and concentration inequalities, Brunn-Minkowski type inequalities and Khinchine inequalities.
Full description:	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
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).
Learning outcomes:	1. Student knows and understands basic inequalities in convex geometry. 2. Student knows and is able to use basic proof techniques.
Assessment methods and 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).

Classes in period "Summer semester 2023/24" (in progress)

Time span:	2024-02-19 - 2024-06-16	Selected timetable range: weekly course term Navigate to timetable MO TU WYK-MON W CW TH FR
Type of class:	Classes, 30 hours more information Monographic lecture, 30 hours more information
Coordinators:	Piotr Nayar
Group instructors:	Daniel Murawski, Piotr Nayar
Students list:	(inaccessible to you)
Examination:	Examination

Course descriptions are protected by copyright.
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