Ce livre constitue un expose detaille de la serie de cours donnes en 2020 par le Prof. Nicolas Bergeron, titulaire de la Chaire Aisenstadt au CRM de Montreal. L'objet de ce texte est une ample generalisation d'une famille d'identites classiques, notamment la formule d'addition de la fonction cotangente ou celle des series d'Eisenstein. Le livre ......
Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often ......
This book provides an introduction to classical methods in commutative algebra and their applications to number theory, algebraic geometry, and computational algebra. The use of number theory as a motivating theme throughout the book provides a rich and interesting context for the material covered. In addition, many results are reinterpreted from ......
"We completely compute the slice spectral sequence of the C4-spectrum BP((C4))(2). This spectrum provides a model for a height-4 Lubin-Tate theory with a C4-action induced from the Goerss-Hopkins-Miller theorem. In particular, our computation shows that EhC124 is 384-periodic"--
Ricci flow is an exciting subject of mathematics with diverse applications in geometry, topology, and other fields. It employs a heat-type equation to smooth an initial Riemannian metric on a manifold. The formation of singularities in the manifold's topology and geometry is a desirable outcome. Upon closer examination, these singularities often ......
This textbook bridges the gap between lower-division mathematics courses and advanced mathematical thinking. Featuring clear writing and appealing topics, the book introduces techniques for writing proofs in the context of discrete mathematics. By illuminating the concepts behind techniques, the authors create opportunities for readers to sharpen ......
This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains ......
The Mathematical Neighborhoods of School Mathematics visits regions beyond, but proximal to and accessible from school mathematics. Its aim is to give readers a glimpse of not just the rich diversity and adaptability of mathematics, but, most importantly, its interconnections and overall coherence, a perspective not easily available from the ......
