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Applications of harmonic analysis to Discrete Geometry

Grant number: 17/25237-4
Support type:Scholarships in Brazil - Doctorate
Effective date (Start): March 01, 2018
Effective date (End): July 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Theory of Computation
Principal researcher:Sinai Robins
Grantee:Fabrício Caluza Machado
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil


This is a PhD research project for Fabrício Caluza Machado, to be developed under the supervision of professor Sinai Robins at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP). This proposal includes the following problems in Discrete Geometry: the maximization of volumes of inscribed polytopes in a sphere, discrete analogues of volumes of polytopes, packing problems in Euclidean space and on the sphere, and distance-avoiding sets. An example of discrete volume is the number of integer points inside a given polytope, but other possibilities involve assigning more general weights to the points of a lattice. The unifying theme between the problems to be considered is the usage of Fourier methods, for example the Fourier transform and the Poisson summation formula, that allows one to use analytic tools in the study of these geometric problems. (AU)

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Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
MACHADO, Fabrício Caluza. Applications of harmonic analysis to discrete geometry. 2021. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.

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