Beijing Institute of Mathematical Sciences and Applications

We will continue to study magnitude homology and other concepts related to it. In particular, we will study the concept of magnitude cohomology algebra, and show that a finite metric space is uniquely determined by this algebra. We will also study the concept of reachability homology to which a magnitude-path spectral sequence converges; and the spectral homology of quasimetric spaces that generalize the pages of this spectral sequence. We will also touch on the analytical aspects of the theory of magnitude, and analyze the calculation of the magnitude function of an odd-dimensional ball.