Palestrante: Fernando Nóbrega (Universidade de Amsterdã)

Data: 12 de Janeiro de 2026 às 15h

Resumo: In this talk, we will show how we apply the phenomenological renormalization group to resting-state fMRI time series of brain activity in a large population. By recursively coarse graining the data, we compute scaling exponents for the series variance, log probability of silence, and largest covariance eigenvalue. The scaling exponents clearly exhibit linear interdependencies in the form of scaling relations and inherent variability of values closely related to the structure of correlations of brain activity. The scaling relations between the exponents are derived analytically. We find a significant correlation of exponents with clinical (gray matter volume) and behavioral (cognitive performance) traits. Akin to scaling relations near critical points in thermodynamics, our results suggest that this interdependency is intrinsic to brain organization, and may also exist in other complex systems.

D. M. Castro, E. P. Raposo, M. Copelli, F. A. N. Santos, Interdependent scaling exponents in the human brain,  

Physical Review Letters 135, 198401 (2025).

Palestrante: José Luando de Brito Santos (Universidade Estadual da Paraíba)

Data: 26 de Fevereiro de 2026 às 10h

Resumo: In this talk, we will discuss the existence of positive solutions for certain classes of Schrödinger equations involving double weighted nonlocal interaction with a potential that may vanish at infinity. We consider both the case of a general nonlinearity with subcritical growth that satisfying suitable conditions, and the critical homogeneous case in the sense of the Stein–Weiss inequality. To obtain our results, we employ variational methods combined with a truncation argument, the penalization technique of Del Pino and Felmer, and Moser’s iteration method. 

Palestrante: Denílson da Silva Pereira  (Universidade Federal de Campina Grande)

Data: 26 de Fevereiro de 2026 às 11h

Resumo: We establish a new abstract minimax theorem for obtaining ground-state critical points of a class of C1-functionals. The central feature of this class is that the associated Nehari set is not necessarily a differentiable manifold, but is homeomorphic to a (possibly non-complete) submanifold of the unit sphere. This occurs for functionals whose fibering maps t 7→ I(tu) possess a unique global maximum point only when u belongs to an open cone in the underlying Banach space. A detailed topological analysis of the Nehari set is conducted to overcome the lack of a standard variational framework on it. As a consequence, we provide a general minimax characterization of the ground-state energy level. The applicability and robustness of our abstract results are demonstrated by considering a range of relevant elliptic partial differential equations, leading to improvements and complements of existing results in the literature.