Invited speakers
Confirmed Invited Speakers
Anne Frühbis-Krüger – Universität Oldenburg, Germany
Arun Ross – Michigan State University, USA
Guillermo Peñafort – University of Valencia, Spain
Irma Palláres Torres – University of Cantabria, Spain
José Luis Cisneros Molina – UNAM, Mexico
Laurentiu Maxim – University of Wisconsin, USA
Ketty A. de Rezende - University of Campinas Brazil
Miriam Manoel – University of São Paulo (USP), Brazil
Raimundo Nonato Araujo dos Santos – University of São Paulo (USP), Brazil
Abstracts
José Luis Cisneros Molina
Title: Milnor Fibration Theorem: an overview
Abstract: Milnor’s fibration theorem is a landmark in singularity theory, it allowed to deepen the study of the geometry and topology of analytic maps near their critical points. To each singular point of a complex hypersurface it associates a fibre bundle, known as the Milnor Fibration of the singularity. In this talk we will give an overview of this important theorem, in its complex and real versions, and some of its generalizations.
Ketty A. de Rezende
Title: Singularity Collisions in Gutiérrez–Sotomayor Flows
Abstract: Gutiérrez–Sotomayor singular flows, introduced six years ago, have attracted considerable attention for exhibiting invariant sets that include regular, cone, Whitney, double, and triple point singularities. In this joint work with D. Tenário and D. Lima, we employ Conley’s homotopy index together with a spectral sequence analysis of a filtered Gutiérrez–Sotomayor chain complex to classify the types of singularity collisions that arise under homotopical deformations of the flow. Moreover, we establish a theorem describing the local dynamics along the collision path, demonstrating the emergence of an anti-flow at the moment of collision.
Laurentiu Maxim
Title: Singularities and optimization
Abstract: I will explain how various facets of singularity theory can be used to understand the algebraic optimization degrees for linear optimization and the nearest point problem.
Miriam Manoel
Title: Uncovering Symmetry: Algebraic Tools and Their Role in Dynamical Systems
Abstract: Symmetry is everywhere in mathematics and science: from the patterns of crystals in nature to the laws that govern physical systems. But how can we systematically describe and use symmetry in mathematical models? In this talk, I will introduce algebraic tools that allow us to compute and organize the building blocks of functions and vector fields that respect the symmetry of a system. These tools make it possible to design algorithms that reveal how symmetry shapes the behavior of dynamical systems, including how they evolve, bifurcate, or develop singularities. Through examples, I will show how abstract algebra can be transformed into a practical toolkit for studying dynamics with symmetry. The results I will present are the outcome of enjoyable and productive collaborations with P. Baptistelli (UEM, Brazil), F. Antoneli (UNIFESP, Brazil), and A. P. Dias (UP, Portugal).
Guillermo Peñafort
Title: Topology of deformations of finite mappings via cubical hyperresolutions
Abstract: Given a map-germ f : (Cⁿ, S) → (Cᵖ, 0), we study the topology of the image of a small perturbation fδ of f. A classical tool for this purpose is the Image Computing Spectral Sequence, introduced by Goryunov and Mond, which computes the cohomology of the image from the alternating cohomology of the multiple-point spaces of fδ. We introduce a simpler alternative based on cubical augmentations of Xδ. Using the machinery of cubical hyperresolutions, we recover classical results and obtain new ones. This is joint work with José Galindo.