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Applications of singularity theory: differential geometry and algebraic geometry

Grant number: 16/14580-7
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): March 01, 2017
Effective date (End): May 31, 2019
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Farid Tari
Grantee:Juan Viu Sos
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

The project has two lines of research in applications of singularity theory to differential geometry and to algebraic geometry. In the first line of research, our purpose is to investigate the Minkowski Symmetry Sets of surfaces in the Minkowski 3-space and to seek Minkowski analogues of Damon's results on skeletal structure. Challenges arise at the locus of points on the surface where the induced pseudo-metric is degenerate. However, as we showed in our previous work, singularity theory approach to problems involving degenerate pseudo-metrics can lead to surprising results. The second line of research is inspired by the beneficiary's results in his PhD thesis and will focus on the the study of logarithmic vector fields on affine and projective line arrangements. There are also other problems of interests on periods of Kontsevich-Zagier using resolutions of singularities. (AU)

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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)
BARTOLO, ENRIQUE ARTAL; GUERVILLE-BALLE, BENOIT; VIU-SOS, JUAN. Fundamental Groups of Real Arrangements and Torsion in the Lower Central Series Quotients. EXPERIMENTAL MATHEMATICS, v. 29, n. 1, p. 28-35, . (17/15369-0, 16/14580-7)
VIU-SOS, JUAN. A semi-canonical reduction for periods of Kontsevich-Zagier. INTERNATIONAL JOURNAL OF NUMBER THEORY, v. 17, n. 01, p. 147-174, . (16/14580-7)
GUERVILLE-BALLE, BENOIT; VIU-SOS, JUAN. Configurations of points and topology of real line arrangements. MATHEMATISCHE ANNALEN, v. 374, n. 1-2, p. 1-35, . (17/15369-0, 16/14580-7)

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