AbstractThe curvature tensor captures the essential geometry of a Riemannian manifold. Curvaturebounds have important geometric, analvtical and topoloaical conseauences, in tum. these can beused for axiomatic characterizations of curvature bounds and extended to general metric spaces.Problems of modemn data analysis lead to a new perspective on curvature that will bedeveloped in this lecture, a...
Speakery research focuses on mathematical analysis, algorithm development, and their applications in machine learning and scientific computing, spanning both data and physical sciences. My Ph.D. training was grounded in classical numerical methods for partial differential equations (PDEs), with a particular emphasis on finite element methods (FEM) and multigrid methods. Armed with this solid fo...