CV Lattes
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Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC) (Institutional affiliation from the last research proposal) Birthplace: Brazil
Willian Hans completed his highschool at Colégio Uniesp Objetivo de Presidente Epitácio in 2009, the Bachelor Degree in Mathematics at Instituto de Matemática e Estatística da Universidade de São Paulo (IME - USP) in 2013, and a PhD in Mathematics at Instituto de Matemática e Estatística of Universidade de São Paulo (IME - USP) in 2018, under the advising of Valentin Ferenczi, with a period in Universidad de Extremadura, under supervision of Jesús Castillo, funded by Program PDSE/Capes. He did his postdoctorate at Universidade de São Paulo, under the supervision of Valentin Ferenczi, and at Universidad Complutense de Madrid, under supervision of Carloz Palazuelos. Currently he is a professor at ICMC - USP. (Source: Lattes Curriculum)
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The theory of interpolation of Banach spaces arose from the need to prove the continuity of certain operators defined on $L_p$ spaces, being generalized to the study of operators in Banach spaces in general. An interpolation scale between $X_0$ and $X_1$ can be seen as a deformation of the space $X_0$ to the space $X_1$, and the intermediate spaces have properties that, in general, merge …
The theory of Muckenhoupt weights allows us to characterize when Calderón-Zygmund operators are bounded on weighted Lp spaces. A consequence of that theory is the celebrated Coifman-Rochberg-Weiss Commutator Theorem, which states that the commutator between a BMO function and a Calderón-Zygmund operator is always bounded on Lp (p strictly greater than 1 and finite). The objective of this …
The Brunn-Minkowski inequality is an important result of geometry, which relates the volume of two compact subsets of Euclidean space. In this work we will study a reverse version of these inequality, obtained using the theory of interpolation and quasi-normed spaces, obtained by Bastero, Bernués and Peña, and that extends results of Pisier.
Questions of lineability and spaceability seek to understand when we can find a vector space or Banach space in a given set, initially without requiring much structure in the set. One step further is to look for a copy of a specificBanach space. The current project aims to study results regarding the possibility of finding copies of c0 in the set SNA(M) of all Lipschitz functions from a p…
A twisted sum of two Banach spaces Y and Z is a quasi-Banach space X which has a subspace isomorphic to Y with respective quotient isomorphic to Z. When Y and Z are Hilbert spaces X is said to be a twisted Hilbert. Few examples of twisted Hilbert are known, and in this project we intend to find other examples, conditions for singularity (Y being the most non-complemented in X) e for other…
Our purpose is to study some papers in subjects such that Topology, Linear Algebra, indeed, Functional Analysis. We also propose the study of a very beautiful and useful James Theorem, which means some characterizations of reflexive Banach space.(AU)
The study of interpolation theory motivates the concept of analytic family. These families try to capture the notion of an analytic function which values are Banach spaces, and they arise naturally when we study the complex interpolation methods for pairs and families of Banach spaces. We are interested in what corresponds to the process of differentiation of those families, which generat…
Information theory deals with the storage and transmission of information. Quantum mechanics allowed the use of new resources to this area: in the classical model the unit of information is a bit, which assumes values 0 or 1, while in the quantum version the unit of information is a qubit, which assumes any value in the complex sphere. This is justified by the fact that in quantum mechani…
| 1 / 1 | Ongoing grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 2 / 2 | Completed scholarships in Brazil |
| 2 / 2 | Completed scholarships abroad |
| 8 / 8 | All research grants and scholarships |
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