Tingley’s Problem(s): Positive answers and insightful results

Start: 10 October 2025 09:00
End: 10 October 2025 10:00
Categories: Conference , Seminar , Instituto de Matemáticas UGR

Where: Seminario Analisis Matematico, Facultad de Ciencias

IMAG Functional Analysis Seminar
Title: Tingley's Problem(s): Positive answers and insightful results
By Pedro Saavedra Ortiz (UGR)
Abstract: Banach spaces play a key role in mathematics due to their structural richness and wide applications. Classical results link isometries of normed spaces, unit balls, and spheres to linear isometries, with Tingley's Problem (1987) focusing on whether sphere isometries extend isometrically and R-linearly - a question still open in dimensions ≥ 3. A variant of this problem studies spheres of positive elements, reducing even further the available information about the considered spaces. In this talk, we will show the interplay between Algebra, Analysis and Geometry that is suggested by Tingley's Problem, and we will explore some of the tools utilised to provide a positive answer in certain spaces (such as C(K) with K compact or JBW*-algebras).