About
I am a mathematician at the Universidad de Talca, Chile, working at the intersection of representation theory and algebraic combinatorics.
I received my PhD in Mathematics from the Universidad de Talca under the supervision of Dr. David Plaza. My academic path began at the Universidad del Bío-Bío, where I qualified as a mathematics teacher, and continued with a Master's degree and a PhD at the Universidad de Talca.
My doctoral studies were funded by the ANID National Doctoral Scholarship and included a research stay at the Université de Picardie Jules Verne in France. At the Universidad de Talca I have taught courses ranging from Calculus and Linear Algebra to Advanced Geometry.
- PhD in Mathematics
- Universidad de Talca · advisor Dr. David Plaza
- Research stay
- LAMFA, Université de Picardie Jules Verne, France
- Funding
- ANID National Doctoral Scholarship
- Earlier studies
- MSc, Universidad de Talca · Teaching degree, Universidad del Bío-Bío
Research
My interests lie in the representation theory of Hecke algebras, algebraic combinatorics and Kazhdan–Lusztig theory. I study the algebraic structures of Coxeter groups and affine Weyl groups, with a particular focus on positivity properties of bases and the combinatorics of the Bruhat order.
Doctoral thesis
The thesis studies affine Weyl groups and Kazhdan–Lusztig polynomials through the elements θ(λ) and a family of bases of the spherical Hecke algebra called pre-canonical bases. Its central result is a proof of the positivity conjecture for these bases in type Ãn, obtained through a combinatorial approach based on M-elements, including techniques for M-elements with negative indices and an inversion method built on combinatorial filters.
Publications
Talks
Organization
Interactive animations4 animations
Step-by-step procedures from my research: alcoves of affine Weyl groups, Kazhdan–Lusztig bases and pre-canonical bases. Each one runs in the browser and can be manipulated with the mouse.
Coloring the alcoves
The alcove arrangement colored by the walls s₀, s₁, s₂: labels by left multiplication, length as separating hyperplanes, the dominant cone and the elements θ(λ).
Open animation →
The Kazhdan–Lusztig basis
The algorithm HsHx′ − Σ μ Hz drawn on the alcoves: coefficients crossing walls, constant terms removed, and hy,x for any x and y you click.
Open animation →
Spherical and antispherical modules
Kazhdan–Lusztig polynomials hμ,λ computed in the dominant cone; at v = 1 they give the weight multiplicities of V(λ). The antispherical option gives Soergel’s ny,x.
Open animation →
Pre-canonical bases in type A
Partitions and weights, λ − ΣI and straightening, the operators P, Q, v, P, v on your own λ, and a worked example in A6 where a good pair expands and a bad pair cancels out.
Open animation →Teaching
I teach undergraduate mathematics for engineering, science, health and teacher-training programs. My aim is to make fundamental mathematical structures understandable and to connect them with problem solving.
Courses taught
Lecture notes
In Spanish, for my students.
¿Eres o fuiste mi estudiante?Material de todos los cursos, tus notas del semestre, talleres en vivo y práctica: ingresa con tu matrícula.
Ir al portal de estudiantesPhotography
Contact
Universidad de Talca
Talca, Chile