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Geometry, topology and data science

Grant number: 22/09891-4
Support Opportunities:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): September 01, 2022
Status:Discontinued
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Acordo de Cooperação: ANR
Principal Investigator:Henrique Nogueira de Sá Earp
Grantee:Tomas dos Santos Rodrigues e Silva
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:21/04065-6 - BRIDGES: Brazil-France interplays in Gauge Theory, extremal structures and stability, AP.TEM
Associated scholarship(s):23/11699-7 - Machine learning G2 structures, BE.EP.DD

Abstract

This doctorate research project will address the application of machine learning techniques to problems in complex differential and algebraic geometry. On a first track, the candidate will study the technique proposed in [AHO20] for machine learning the Calabi-Yau metric on projective threefolds; and will try to adapt this technique to numerically produce special G_2-metrics on the 7-manifolds studied in [CADE20]. On a second track, inspired by the process presented in [DVB+20] of machine learning potential patterns and relationsbetween mathematical objects, the candidate will try to computationally approach the construction of examples and counterexamples to some open problems in algebraic geometry, such as the Terao and Hartshorne conjectures. (AU)

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