Conférences  >  Mathématiques  >  Analyse  >  États-Unis

American Mathematical Society and Georgia Southern University-Armstrong Campus

The interaction between topology and curvature is a fundamental theme in modern mathematics. The study of scalar curvature plays an increasingly important role not only in geometry and topology, but also in general relativity and theoretical physics more generally through the theory of Dirac operators. This special session will bring together experts and young researchers who study these topics from many different points of view. The aim of this session is to share viewpoints and progress on understanding the scalar curvature and topology of manifolds, and to establish new connections among the culturally diverse groups spread worldwide, but particularly in the USA.

Email.: ekanshjauhari@ufl.edu

Global Riemannian geometry, curvature restrictions, differential geometric analysis, index theory, spin geometry, algebraic topology of manifolds.

Géométrie et topologie,    Physique mathématique

Formalization of mathematics is the process by which pen-and-paper mathematics is translated into a strict chain of logical deductions down to the axioms of mathematics. The subject has seen renewed interest in the last decades, thanks to the development of computer systems, called proof assistants, which make this feasible in practice. There have now been several examples of high-profile mathematical results which have been formalized. In principle any mathematical domain is accessible, but existing projects are skewed towards algebra instead of analysis. Notable exceptions are a project which formalized enough of Gromov’s convex integration theory to deduce Smale’s sphere eversion theorem, and the ongoing project to formalize Carleson’s convergence theorem for Fourier series. This workshop will bring together formalization experts and interested mathematicians to give a new impulse to formalization of analysis (in a very broad sense), and to develop abstractions and tools to deduplicate effort.

Tél.: [4018635030];     Email.: info@icerm.brown.edu