Geometric Functional Analysis and Probability Seminar

Date:
11
Thursday
December
2025
Lecture / Seminar
Time: 13:30-14:30
Title: Generalized Hodge theory for geometric boundary-value problems
Location: Jacob Ziskind Building
Lecturer: Roee Leder
Organizer: Faculty of Mathematics and Computer Science
Contact: hany.kochavi@weizmann.ac.il
Details: HUJI
Abstract: A fundamental theorem states that a two-dimensional Riemannian manifold with bou ... Read more A fundamental theorem states that a two-dimensional Riemannian manifold with boundary, equipped with a symmetric tensor field, is locally isometrically embedded in Euclidean space if and only if the symmetric tensor field satisfies the Gauss-Mainardi-Codazzi equations—in which case, the tensor field is the second fundamental form. When the intrinsic metric is Euclidean, it is a classical result that such tensor fields are Hessians of functions satisfying the Monge-Ampère equation. I shall present a version of this result to arbitrary Riemannian metrics, using a generalized Hodge theory I developed for a broader class of geometric boundary-value problems. I will discuss this theory, its main features, and perhaps give a glimpse of more complicated examples it addresses.
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