Equipped with the L2,q-distortion distance 𝚫2,q, the space 𝕏2,q of all metric measure spaces (X, ?, 𝔪) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on ?𝕏2,q are ......
It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the ......
It appears to me that if one wants to make progress in mathematics one should study the masters and not the pupils."" -Niels Henrik Abel Recent pedagogical research has supported Abel's claim of the effectiveness of reading the masters. Students exposed to historically based pedagogy see mathematics not as a monolithic assemblage of facts but as a ......
This volume contains the proceedings of the Conference on Compactifications, Configurations, and Cohomology, held from October 22-24, 2021, at Northeastern University, Boston, MA. Some of the most active and fruitful mathematical research occurs at the interface of algebraic geometry, representation theory, and topology. Noteworthy examples ......
Residue theory is an active area of complex analysis with connections and applications to fields as diverse as partial differential and integral equations, computer algebra, arithmetic or diophantine geometry, and mathematical physics. Multidimensional Residue Theory and Applications defines and studies multidimensional residues via analytic ......
This volume contains the proceedings of the 2017 Georgia International Topology Conference, held from May 22-June 2, 2017, at the University of Georgia, Athens, Georgia. The papers contained in this volume cover topics ranging from symplectic topology to classical knot theory to topology of 3- and 4-dimensional manifolds to geometric group theory. ......
It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the ......
This volume contains the proceedings of the virtual conference on Cyclic Cohomology at 40: Achievements and Future Prospects, held from September 27-October 1, 2021 and hosted by the Fields Institute for Research in Mathematical Sciences, Toronto, ON, Canada. Cyclic cohomology, since its discovery forty years ago in noncommutative differential ......
