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