ELIDEK: Geometric Functional Analysis and High Dimensional ProbabilityGFAHDP 15445.
General Discription: The aim of this proposal is to study geometric problems in high-dimensional spaces from a functionalanalytic and/or probabilistic point of view. We explore powerful methods from the field of geometricfunctional analysis that successfully interact with several areas including high-dimensional probability,harmonic analysis and convex geometry. High dimensional structures appear in a variety of branches ofmathematics and adjacent sciences; in particular, physics and computing. The methods of geometricfunctional analysis and high-dimensional probability enable us to understand their typical behavior andto describe their basic features mathematically. In this sense, we expect that progress in the directionsof the proposed research will be very useful for researchers working in a broad interdisciplinary area.During this project, and by its very nature, the research group will develop strong links with severalinstitutes and research centers. It is expected that this interaction will continue and flourish in thefuture, and will contribute greatly to the coordination and synergy with international interdisciplinaryactivities.A third main goal of the proposal is to support young researchers. The postdoctoral and/orpredoctoral researchers who will be involved in the project will have exposure to a variety of influencesand will identify contemporary research fields in which they might work in the future. The project willenable to strengthen and complement the geometric functional analysis group in the country, helpingin the establishment of a critical mass of researchers.Our main directions of research are:(i) Extremal volume sections and projections convex bodies.(ii) Isoperimetric-type inequalities and connections to harmonic analysis.(iii) Random and extremal high-dimensional discrete structures.(iv) MM∗-estimates and geometric applications.
Ερευνητική Ομάδα: Μόνιμα Μέλη Πανεπιστημίων: Σιλoυανός Μπραζιτίκος (Πανεπιστήμιο Κρήτης)-Επιστημονικά ΥπεύθυνοςΑπόστολος Γιαννόπουλος (ΣΕΜΦΕ-ΕΜΠ)Αλέξανδρος Εσκενάζης (Sorbonne Universite-Paris)Tomasz Tkocz (Carnegie Mellon-Pittsburgh)Μαρίνα Ηλιοπούλου (Μαθηματικό Τμήμα-ΕΚΠΑ)
Μεταδιδακτορικοί Ερευνητές:Γεώργιος ΧασάπηςΔημήτρης-Μάριος Λιακόπουλος
Διδακτορικοί Ερευνητές:Ναταλία Τζιώτζιου Χρήστος Πανδής