Speaker: Juan José Maulén
Center for Mathematical Modeling, U. de Chile
Date: Tuesday, May 19, 2026 at 2:00 p.m. Santiago time
Abstract:
TBA
Venue: Sala John Von Neumann, 7th floor, Beauchef 851
All posts by mcantarino
A glimpse about blow-up algebras
Speaker: André Dosea
Universidade Federal de Sergipe
Date: Tuesday, May 05, 2026 at 2:00 p.m. Santiago time
Abstract:
Blow-up algebras is a classical and central topic in both commutative algebra and
algebraic geometry. From the geometric point of view, they appear related to the Theory of Resolution of Singularities. On the algebraic side, they are mostly used to capture the algebraic relations between generators of some ideal. This is a very intuitive problem that can be roughly translated in terms of computing the implicit equations of a parametric curve or a parametric surface.
In this talk, we present through examples two of these Blow-up Algebras: The Rees Algebra and the special fiber of an ideal. We discuss the challenging problem of finding the defining equations of these algebras, highlighting some new results and open problems.
Venue: Sala John Von Neumann, 7th floor, Beauchef 851
The Hurwitz automorphism problem and its “translation surface” version
Speaker: Julien Boulanger
Center for Mathematical Modeling, U. de Chile
Date: Tuesday, April 28, 2026 at 2:00 p.m. Santiago time
Abstract:
In 1893, Hurwitz showed that a compact Riemann surface of genus g ≥ 2 has at most 84(g-1) automorphisms. This bound is optimal for an infinite family of genera but there is also an infinite family of genera for which the bound is not optimal. The Hurwitz automorphism problem consists in finding the optimal bound for every genus, and apart from partial results in specific cases it is far from being solved. In this talk we will explain the first sentence of this abstract and give a geometric intuition for the result. On the way, I will discuss a similar problem for translation surfaces.
Translation surfaces can be seen a Riemann surfaces with an additional structure, and an automorphism of a translation surface must preserve this additional structure: in particular, there are even less automorphisms and a compact translation surface of genus g ≥ 2 has at most 4(g-1) automorphisms. This last bound was obtained by J.C. Schlage-Puchta and G. Weitze-Schmidhüsen in 2013, and they also show that the bound is optimal if and only if g-1 is either even or a multiple of 3. In a joint work with R.Gutierrez-Romo and E.Lanneau, we study the other cases and provide the optimal bound for example when g = pq+1 with p,q ≥ 5 prime numbers.
Venue: Sala John Von Neumann, 7th floor, Beauchef 851