Campinas
Campinas
São Carlos
São Carlos
Algebra and Geometry meeting
Algebra and Geometry meeting
ICMC, São Carlos, November 6, 2026
This one-day event brings together researchers in Algebra and Geometry from Sao Carlos and Campinas.
There will be invited talks and a poster session. Registration open here.
Gabriel Fazoli
Kaique Matias de Andrade Roberto
Otavio Perez
Vincent Grandjean
Yulia Gorginian
Zhengning Hu
TBA
Gabriel Fazoli - IMECC - Applications of the First Transverse Jet of an Invariant Curve
In this talk, we study invariant algebraic curves of foliations on algebraic surfaces. An invariant curve carries a natural flat partial connection, whose first transverse jet allows us to study singularities of the curve and of the foliation. Using the associated local indices, we recover the Cerveau–Lins Neto degree bound for smooth invariant curves. We also discuss a rigidity phenomenon: when a scheme naturally associated to this construction has sufficiently small length, the foliation admits an invariant line and, under suitable hypotheses, a rational first integral.Kaique Matias de Andrade Roberto - CLE - Generalized Marshall Quotients and Real Semigroups of Continuous and Differentiable Functions
The theory of real semigroups developed by M. Dickmann and A. Petrovich provides an algebraic framework for abstract real spectra and real algebraic geometry, yet its application to rings of continuous functions is historically hindered by the topological constraints. In this talk, I bridge this gap by introducing generalized Marshall quotients over rings of real-valued continuous and differentiable functions, yielding new explicitly calculated examples of real semigroups. Furthermore, we conclude that the group of invertible elements of these quotients constitutes a real reduced hyperfield (which is categorically equivalent to reduced special groups), addressing the open problem of characterizing when the units of a real semigroup form a reduced special group. Finally, we apply this hyperalgebraic machinery to translate topological and differential phenomena into hyperalgebraic identities, establishing generalized versions of the Lojasiewicz-type inequalities.Otavio Perez - ICMC - Generalized upper principal part of real planar polynomial vector fields
The goal of this paper is to generalize recent results about the topological classification of the dynamics of a real planar polynomial vector field near infinity. Given a polynomial vector field $X$, using Newton polyhedra one can define its generalized upper principal part $X_{\Gamma}^{U}$. By dropping some monomials of $X_{\Gamma}^{U}$, we define its minimal generalized upper principal part $X_{G}^{U}$. We prove that there exist an open and dense set $\widetilde{\mathfrak{U}}_{1}$ in the set of polynomial vector fields with Newton degenerate upper principal part satisfying the following property: if $X\in\widetilde{\mathfrak{U}}_{1}$, then $X$ and $X_{G}^{U}$ are topologically equivalent near infinity, provided that $X_{G}^{U}$ satisfies some additional non-degeneracy assumptions. Our techniques rely on toric compactification and the Normal Form Theorem. Joint work with Thaís Maria Dalbelo and Regilene Oliveira.Vincent Grandjean TBA
Yulia Gorginian TBA
Zhengning Hu - IMECC - Rational Chow groups of Hurwitz spaces
The Hurwitz space, parametrizing degree d genus g covers of the projective line up to automorphisms of the target, is a fundamental tool in the study of moduli spaces of curves. In this talk, we shift the focus to the intersection theory on the Hurwitz space itself, and its admissible covers compactification. We will discuss various intersection-theoretic techniques used in computing their rational Chow groups/rings, particularly in the context of double, triple and quadruple covers.