"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. Ther…
Incidences and classical discrete geometry -- Basic real algebraic geometry in R² -- Polynomial partitioning -- Basic real algebraic geometry in Rd -- The joints problem and degree reduction -- Polynomial methods in finite fields -- The Elekes-Sharir-Guth-Katz framework -- Const…
The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdős's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. Ther…
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
"The past decade has seen numerous major mathematical breakthroughs for topics such as the finite field Kakeya conjecture, the cap set conjecture, Erdös's distinct distances problem, the joints problem, as well as others, thanks to the introduction of new polynomial methods. The…
This monograph arose from lectures delivered by the authors at the Winter School "Operator Spaces, Noncommutative probability and Quantum Groups", December 1-12, 2014, held at the Azuréva Métabief in the Jura Mountains in France.
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisel…
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precise…
This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute of Mathematics and its Applications during the Spring 2015 where geometric analysis, convex geometry and concentrat…
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined a…
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined a…