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ADVANCED ANALYSIS A

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2023/2024
Year: 
1
Academic year in which the course will be held: 
2023/2024
Course type: 
Compulsory subjects, characteristic of the class
Credits: 
8
Period: 
First Semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

Analysis 1,2,3 Linear Algebra, Probability

Final Examination: 
Orale

Verification of learning will be carried out with an oral test regarding the topics covered in the course

Assessment: 
Voto Finale

Knowledge of the main results of the measurement concentration phenomenon with its main applications to dimensional reduction, the geometry of convex bodies and the "compressed sensing" theory

Main probabilistic inequalities, isoperimetric problems, measurement concentration, dimensional reduction and theory of convex bodies.

Standard inequalities in probability: Markov, Chebyshev, Chernoff and Hoeffding.
Introduction to sub-gaussian random variables. Johnson-Lindenstrauss lemma: Gaussian e sub-gaussian version. Introduction to Haar measure. Invariant measure on n-dimensional sphere. Pull-forward measures. Ellipsoids and convex bodies. Minkowski functional. The John ellipsoid. Concentration function and the isoperimetric problem. Dvoretsky theorem. Compressed sensing. Kashin decomposition method.

Classroom lections

Meetings by appointment

Professors

CASINI EMANUELE GIUSEPPE

Borrowers