Geometry, Singularities, and Differential Equations: Exploring Mathematical Complexity

Débora Lopes da Silva, UFS

Abstract:

The term "singularity" frequently appears in various fields and with different meanings. In mathematics, singularity theory addresses several fundamental questions: What types of singular models exist? Given a model with a singularity, what happens if we perturb it? Does the singularity disappear or does its type change? Do these singular models possess algebraic structures? How do they behave, and how significant are they in the realm of all possible models? In general, these questions are quite challenging to answer. However, understanding them is crucial for advancing our knowledge of singularities. In this talk, we will explore various aspects of singularity theory, aiming to reveal the fascinating universe of ideas that emerge from this field, applying it to the classification of different types of singularities that arise in mathematics.