CV Lattes
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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Peru
Graduated in Mathematics - Universidad Nacional Mayor de San Marcos (2013), master's degree in Mathematics from the University of São Paulo-São Carlos (2017), research internship at CINVESTAV-IPN, Mexico (2019-2020) and PhD in Mathematics from the University from São Paulo-São Carlos (2022). He has experience in the area of Mathematics, focusing mainly on the following topics: Algebraic Topology: Topological Complexity, Lusternik-Schnirelmann Category, Sectional Category, Configuration Spaces, Borsuk-Ulam Theory, Fixed Point Theory, G-equivariant Theory and G-equivariant maps, Coincidence Theory, Cohomology Ring and Category Theory. Applied Algebraic Topology: Robot Motion Planning Problem, Social Choice Theory, Topological Data Analysis (TDA) and Medical Research Topics. Singularity Theory: Milnor Fibration. Group Theory: Configurations of a group, coverage number of a group and Sectional number of a group homomorphism. Graph Theory: Chromatic Number, Graph Complexity and Sectional Number of a graph homomorphism. (Source: Lattes Curriculum)
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The present research project has as its goal the construction of foundations of sectional theory in category theory and build bridges between important areas in mathematics. Specifically, this project consists of the following important problems in the field of Geometry and Topology.(1) We define and study a generalization in the category theory setting of the Schwarz genus (it is also kn…
This project deals with questions of spaces of configurations that have consequences in the study of braids and Nielsen's fixed point theory for multivalued functions. It has two sub-cases where one of them is about the configuration space where the manifold has dimension two and another case is when the space has dimension bigger than two. As typical questions that are current and explor…
This project consists of the following important problems in the field of Geometry and Topology:(1) To study the collision free motion planning problem of some important mechanical spaces which appear in robotics. (2) To study the topological complexity of (some) mechanical spaces. (3) To study the variants of topological complexity and related problems. (4) To study the topological compl…
A unified concept of sectional number have been recently introduced by the candidate. He define the $\mathcal{R}$-sectional number $\text{$\mathcal{R}$-sec}$ and the $\mathcal{R}$-mono sectional number $\text{$\mathcal{R}$-msec}$ of a morphism $f$ in a category $\mathcal{C}$ with covers where $\mathcal{R}$ is an equivalence relation over $\text{Mor}_{\mathcal{C}}(c,c^\prime)$ for each $c,…
This research project consists of the followingimportant problems in the area of Geometry and Topology: Compute the topological complexity of ordered and unordered configuration spaces. In particular, compute the topological complexity of braid groups. The topological complexity of braid groups comes at a timely moment after recent and important advances in the description of the topologi…
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