Geometry, topology and data science

• Grant number: 22/09891-4
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: September 01, 2022
• End date: February 28, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: 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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

AGGARWAL, DAATTAVYA; HE, YANG-HUI; HEYES, ELLI; HIRST, EDWARD; EARP, HENRIQUE N. SA; SILVA, TOMAS S. R.. Machine learning Sasakian and G₂ topology on contact Calabi-Yau 7-manifolds. Physics Letters B, v. 850, p. 10-pg., 2024-02-20. (21/04065-6, 22/09891-4, 18/21391-1, 20/09838-0)

HE, YANG-HUI; JEJJALA, VISHNU; SILVA, TOMAS S. R.. Metaheuristic generation of brane tilings. Physics Letters B, v. 862, p. 5-pg., 2025-03-01. (22/09891-4)