Θέμα: Γενικό Σεμινάριο Τμήματος Ομιλία 21/11/24

Το Γενικό Σεμινάριο του Τμήματος συνεχίζεται αύριο, Πέμπτη 21/11/24, ώρα 16:00 - 17:00 στην αίθουσα 342. Η ομιλία θα γίνει στα ελληνικά.

Τα στοιχεία της πέμπτης ομιλίας:

Ομιλητής: Παναγιώτης Γιαννιώτης (Τμήμα Μαθηματικών, ΕΚΠΑ)
Τίτλος: Splitting maps in Ricci flows

Περίληψη: Ricci flow has proven to be a powerful tool in the study of the geometry and topology of 3-manifolds, after the implementation of the surgery procedure for 3d Ricci flow by Perelman 20 years ago. In higher dimensions however it is still unknown how to construct weak solutions of the Ricci flow that continue after a singularity develops. Thus, understanding the formation of the possible singularities seems to be crucial in the implementation of this program.


One question that is still unknown is whether the diameter of the manifold remains uniformly bounded as the flow approaches the singular time. This is still unknown even in dimension three, although it was conjectured by Perelman in 2003 to be true. Such question seems analogous to questions on the size and rectifiability of the singular sets for many other geometric pde. For instance, Cheeger-Jiang-Naber recently showed that the approximate singular set of non-collapsed Ricci limit spaces is rectifiable with uniform bounds on their Hausdorff measure. In their analysis, a central concept is that of a splitting map and the detailed understanding of its behaviour in small scales.


In this talk, after discussing the main background and ideas behind Ricci flow, I will describe an analogue of a splitting map of a Ricci flow, and present some new results on its small scale behaviour for Ricci flows that satisfy a Type I bound on the curvature. Then I will discuss work in progress on how these results relate to Perelman’s conjecture.

Μετά το πέρας της ομιλίας θα υπάρχουν καφές, χυμοί και μπισκότα για τους παρευρισκόμενους.

Εκ μέρους της επιτροπής σεμιναρίου,


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