Affine algebraic and bi-Lipschitz geometry

• Grant number: 25/06706-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: September 01, 2025
• End date: August 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Maria Jadwiga Michalska
• Grantee: Maria Jadwiga Michalska
• Visiting researcher: Zbigniew Jelonek
• Visiting researcher institution: Institute Of Mathematics Of The Polish Academy Of Sciences/Impan, Poland
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 24/04171-9 - Real algebraic geometry with applications, AP.JP

Abstract

Research tasks of the project are in the areas of Algebraic and Lipschitz Geometry and are linked with central problems of the areas. In fact, the project lies nicely in the intersection of areas of interest of the Singularity Group centered in ICMC and the FAPESP project Jovem Pesquisador RAGA, thus allowing for contributions of local specialists while enhancing the Real Algebraic Geometry and Application lines, especially Lipschitz Classification of sets in Tame Geometry and effective Real Algebraic problems. Methods planned in scope of this project rely on singularity theory, algebraic geometry, study of Milnor fiber and explicit constructions, as well as the new methods developed by the brazilian school of Lipschitz geometry. Professor Zbigniew Jelonek is a renowned researcher in Algebraic Geometry with publications in top journals. Though his work is mostly theoretical, its constructive methods leave a relevant impact on areas of applied mathematics such as Optimization theory or Computer Science. The expertise of Zbigniew Jelonek and his regular and impactful production of high quality are strong indicators that significant progress in this project is more than a reasonable expectation.Collaboration, especially with young researchers of ICMC and UFSCar, will be strongly encouraged, emphasizing opportunities of scientific growth of graduate and post-grad students starting their scholarships in the Jovem Pesquisador RAGA project during this stay. Proposed mini-courses and seminar allow for insertion and preparation of students and young researchers in the studyof Real Algebraic and Lipschitz Geometry. The stay overlaps with beginning of planned scholarships inside the project Jovem Pesquisador RAGA. Moreover, during this research stay we plan also visits of André Costa (UECE), Aris Daniilidis (TU Vien) and Vincent Grandjean (UFSC) to fortify colaboration within the RAGA group. Therefore, Zbigniew Jelonek's extended visit is a valuable opportunity for achieving relevant research outcomes and for researchers as well as students in and around Sao Carlos to interact extensively with an internationally renowned expert which will leave a lasting positive mark on the research landscape in SP. (AU)