Next ICTP Associates Seminar: Soap, bubbles and membranes!

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The Associates Office and ICTP Global Science Portal welcome you all to a
hybrid Associates Seminar entitled:

“Stability phenomena in geometry: soap films, bubbles and vibrating
membranes”
given by ICTP Associate Marcos Petrúcio Cavalcante from Instituto de
Matemática, Universidade Federal de Alagoas (UFAL), Brazil.

at 11am CEST, Thursday 1st October in the Stasi room, or online at:
https://zoom.us/meeting/register/9hJpULyeTuOKKvck7sqCgg

Abstract
In the first part of this talk I will tell a little about my path in
mathematics, from my training in differential geometry to building a
research group and a graduate program in Maceió, in the Northeast of
Brazil.
In the second part I will discuss some problems I have worked on in recent
years concerning the shape of geometric objects that arise as critical
points of a functional: soap films, soap bubbles, and domains that are
critical for the fundamental frequency of a vibrating membrane. In each of
these problems the second variation of the functional defines a notion of
stability, together with a Morse index that counts the number of
independent directions in which the object can be improved. A general
principle suggests that stable configurations are simple, both
geometrically and topologically. I will illustrate this principle with
pictures and examples, and then describe two recent results obtained with
coauthors: a lower bound for the Morse index of a compact constant mean
curvature surface in Euclidean space in terms of its genus, and a rigidity
theorem for stable extremal domains of the first Dirichlet eigenvalue on
the round sphere.

ICTP Associates Seminars are part personal, part scientific, with speakers
sharing their career trajectory and experiences, then introducing their
research field and work.

We look forward to seeing many of you there!

Associates Office and ICTP Global Science Portal.