2026 - Semester 1
2026 - Semester 1
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Next talks
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April 14th, 2026
Title: Real version of the Theorem of Nobile
Title: Real version of the Theorem of Nobile
Speaker: Edson Sampaio (UFC)
Abstract: The famous Theorem of Nobile, which is very important in the study and understanding of Nash blow-ups of algebraic varieties, states that the Nash transformation of an algebraic variety X is an isomorphism if, and only if, X is non-singular (over an algebraically closed field of characteristic zero; over prime characteristic, this statement is false). Remember that the Nash transformation (of X) is the restriction of the projection $p: X \times Gr(d,n)\to X$ to the closure of the graph of the Gauss map. Although the Theorem of Nobile has been fundamental in Complex Geometry, the real case remained an open question for 50 years. In this talk, we will present a version of the Theorem of Nobile that holds over the fields of reals and complexes and, in particular, we will see that this important result of Complex Geometry is in fact of a real nature. We will also present a definitive version (with minimal hypotheses) of this theorem.
April 28th, 2026
Title: Singularities of differential operators
Title: Singularities of differential operators
Speaker: Carlos Tomei (PUC-Rio)
Abstract: An example of a differential operator is F(u) = -u'' + u^2, acting on functions satisfying Dirichlet conditions, u(0) = u(1) = 0. The critical set of such functions (between spaces of functions) is stratified by different singularities. The talk will present some situations, with emphasis on a recent result (Ardila, Saldanha,T.): all the singularities of the function F above are Morin singularities, and arbitrarily deep singularities occur. (Joint work with Nicolau Saldanha).
May 12th, 2026
Title: TBA
Title: TBA
Speaker: Bruna Oréfice Okamoto (UFSCar)
Abstract: TBA
2025 - Semester 2
2025 - Semester 2
Dedicated to the memory of
Maria Aparecida Soares Ruas - Cidinha
Dedicated to the memory of
Maria Aparecida Soares Ruas - Cidinha
The Brazilians Singularity Theory Webinar of this semester will be dedicated to the memory of Maria Aparecida Soares Ruas (Cidinha). Her trajectory deeply marked the development of Singularity Theory in Brazil and worldwide, training generations of mathematicians and consolidating research groups that today continue her legacy.
This special series will feature talks by her collaborators, who will present results and perspectives related to her contributions, celebrating the strength and vitality of her work.
Nov 25th, 2025
Title: Bicomplex polar weighted homogeneous polynomials
Title: Bicomplex polar weighted homogeneous polynomials
Speaker: Inácio Rabelo (ICMC-USP)
Abstract: In this talk, we discuss the topology of singularities $\mathbb{R}^{4n} \longrightarrow \mathbb{R}^{4}$ expressed in terms of bicomplex variables and their conjugates. In the first part, we present a bicomplex version of the Milnor fibration theorem and some consequences for the topology of the fibers. In the second part, we introduce an action of nonzero bicomplex divisors and study polynomials that are invariants under this action. This leads to the existence of global and spherical fibrations and to a theorem of Join type. This is a joint work with Yesenia Bravo and Agustín Romano-Velázquez.
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