Lipschitz geometry of stratified spaces

• Grant number: 16/14330-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2016
• End date: February 28, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Aparecida Soares Ruas
• Grantee: Nguyen Xuan Viet Nhan
• 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

We propose to study bi-Lipschitz invariants along strata of some stratifications. O-minimal structures have emerged as an excellent framework for the study of singular spaces. Our focus is on two problems based on some very recent works about the Lipschitz geometry of definable singular spaces in o-minimal structures. The first one asks whether Lipschitz stratification of definable sets in o-minimal structures implies definable bi-Lipschitz triviality along strata of the stratification. The second one is to investigate invariants defined in terms of arc spaces along strata of stratifications, especially, Lipschitz stratifications. (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)

NGUYEN, NHAN; VALETTE, GUILLAUME. WHITNEY STRATIFICATIONS AND THE CONTINUITY OF LOCAL LIPSCHITZ-KILLING CURVATURES. ANNALES DE L INSTITUT FOURIER, v. 68, n. 5, p. 2253-2276, 2018. (16/14330-0)

NGUYEN, NHAN; TRIVEDI, SAURABH. Transversality of smooth definable maps in O-minimal structures. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, v. 168, n. 3, p. 519-533, MAY 2020. (15/12667-5, 16/14330-0)