Where geometry meets analysis
SAGA is a research seminar at IME-USP devoted to Geometric Analysis, Nonlinear PDEs, and their applications. It brings together researchers and students through two complementary tracks.
SAGA
Research-level talks by visiting mathematicians, faculty, and post-docs on geometric PDEs, Riemannian geometry, calculus of variations, and related areas.
SAGA Jr.
Student talks on introductory and exploratory topics. A space for undergraduate and early graduate students to present what they are learning and develop presentation skills.
Schedule & Archive
Upcoming — 2026.2
Extremal surfaces for the first Dirichlet eigenvalue of the Laplacian
Abstract: While many works have investigated extremal domains for the first Dirichlet eigenvalue of the Laplacian, in this talk I will examine the corresponding problem for hypersurfaces, where one varies the immersion rather than the domain inside a fixed ambient manifold. I will present the Euler–Lagrange equation for this variational problem, which links the first eigenfunction to the second fundamental form and leads to both an interior condition and an overdetermined boundary condition. In the minimal and CMC cases, these equations become particularly rigid and impose strong geometric restrictions. As an application, we show that among compact CMC surfaces in the unit ball, the only extremal examples are totally geodesic discs. The proof combines variational analysis and a Hopf differential argument.
Superfícies de Delaunay, geometria e EDOs
Resumo: Apresentamos as superfícies de Delaunay, que são as superfícies de revolução com curvatura média constante. Discutimos a construção clássica via roletas de cônicas, a formulação como sistema de EDOs e a classificação das soluções (undulóides, nodóides, cilindros e esferas).
2026.1
O Problema de Yamabe I: da Curvatura à Geometria Conforme
Abstract: Nesta primeira palestra da série sobre o Problema de Yamabe, apresento uma introdução autocontida partindo das definições de curvatura Riemanniana e derivando a equação de Yamabe em detalhe via mudança conforme da curvatura escalar. Palestras complementares abordarão a resolução histórica e conexões com problemas de prescrição de curvatura de ordem superior.
É possível ouvir o formato de um tambor? Introdução aos problemas da Geometria Espectral
Resumo: Partindo da célebre pergunta de Mark Kac (1966) — é possível ouvir o formato de um tambor? — introduzimos o problema de autovalores do operador de Laplace–Beltrami e deduzimos a equação que os governa, motivando os problemas centrais da Geometria Espectral.
Organizers
João Henrique Andrade
Nonlinear PDEs, Conformal Geometry, Q-curvature, GJMS operators, isolated singularities of geometric equations.
andradejh@ime.usp.br
Eduardo Longa
Riemannian Geometry, minimal and CMC immersions, spectral geometry, extremal metrics for Laplacian eigenvalues.
edulonga@ime.usp.br
Paolo Piccione
Differential Geometry, Riemannian and Lorentzian Geometry, Geometric Variational Problems. Member of the Brazilian Academy of Sciences.
piccione@ime.usp.brHow to Attend
SAGA is open to everyone. No registration required. To propose a talk or suggest a speaker, contact any of the organizers.
Location
Sala A252
Instituto de Matemática, Estatística e Ciência da Computação
Universidade de São Paulo
Rua do Matão, 1010 — Cidade Universitária, SP
Schedule
Biweekly, Fridays
16h – 17h (50 min + discussion)
Selected talks may be streamed online.
Surfaces of Geometric Analysis
Minimal surfaces and their geometric properties are at the heart of SAGA's research themes.
