Upcoming Events
14th Mini Workshop on Singularities, Geometry and Differential Equations
The Mini Workshop on Singularities, Geometry and Differential Equations is a biennial scientific meeting organized by the Singularities Group of São Carlos. Its first edition was held in 1999.
Since its 10th edition, the meeting has also been held outside São Carlos, with the aim of bringing Singularity Theory to other states and regions of Brazil: Fortaleza, Ceará, in 2015; Niterói, Rio de Janeiro, in 2017; and Vitória, Espírito Santo, in 2019. The 13th edition returned to São Carlos, as a joint event of the Universidade Federal de São Carlos and ICMC-USP.
The 14th edition brings the meeting back to the Northeast of Brazil. It will take place in Aracaju, Sergipe, from 4 to 8 October 2027, bringing together researchers and students to share recent results and strengthen collaborations in the field.
Research Lines
Applications of Singularity Theory to Dynamical Systems
Qualitative theory of dynamical systems and bifurcations; algebraic methods applied to bifurcations with symmetry; involutions associated with fold singularities and discrete dynamical systems; cyclicity and criticality, the focus–center problem, limit cycles, and piecewise continuous dynamical systems.
Commutative Algebra, Algebraic Geometry and Singularities
This research area addresses several central themes in Commutative Algebra and their applications to Algebraic Geometry and the Theory of Complex Singularities. Studies concentrate on Commutative Noetherian Rings and Finitely Generated Modules, with an emphasis on Homological Algebra applied to these modules. The research includes characterizations of special classes of modules and rings, such as Cohen-Macaulay Modules, Regular Rings, and Gorenstein Rings. Other central topics encompass the investigation of Auslander-Reiten Conjectures, the calculation and properties of Multiplicities of ideals and modules, and the study of Modules of Differentials and Kähler Differentials. The connections of these topics with Algebraic Geometry and the Theory of Complex Singularities are actively explored. The area also covers the analysis of Rees Algebras, Associated Graded Algebras, and their algebraic structures, and their consequences in singularity theory, in addition to the complex relationships between Theory of Local Blow-ups , and Ramification Theory, including their applications in valuation theory.
Geometric and topological investigation of singularities
Toric actions, Euler obstruction, and Brasselet number; Topology of stable maps and real singularities; Singularities at infinity and global fibrations of polynomial maps; Milnor fibrations of real singularities and regularity at infinity; Cobordism between Morse and generic maps; Differential geometry and singularities.
Classification, equisingularity and invariants
Lipschitz geometry and the bi-Lipschitz theory of singularities; Multiple-point spaces of map germs; Functions defined on singular varieties; Topological and differentiable invariants of singularities; Matrix singularities and determinantal varieties.