While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts ......
We set the foundation for a series of works aimed at proving strong relations between uniform random planar maps and Liouville quantum gravity (LQG). Our method relies on a bijective encoding of site-percolated planar triangulations by certain 2D lattice paths. Our bijection parallels in the discrete setting the matingof-trees framework of LQG and ......
November 11, 2002: Grigori Perelman, a famous mathematician, brilliantly establishes his proof of the Poincare Conjecture. A few years later, he is widely acclaimed for his research. However, he declines the prestigious Fields Medal and persists in not wanting to leave his native city of Saint Petersburg to attend the International Congress of ......
Owing to its simple formulation and intractable nature, along with its application to the lunar theory, the three-body problem has since it was first studied by Newton in the Principia attracted the attention of many of the world's most gifted mathematicians and astronomers. Two of these, Euler and Lagrange, discovered the problem's first periodic ......
This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic ......
Since its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on ......
Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (phi, pi, e and i), each of which has recently been the individual subject of historical and mathematical ......
Topology is the field of mathematics that studies those properties of a shape which persist when the shape gently evolves and changes its specific form. This book gives a playful and intuitive introduction to topology, favoring simple and crisp illustrations over long explanations and formal definitions. The material includes some of the classic ......
