Porter Lectures Series
By János Kollár, Harry Furstenberg, Barry Simon and
()
About this series
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphic functions on hyperelliptic surfaces and the study of covering maps of the Riemann sphere with a finite number of slits removed. This allows for the first book-length treatment of orthogonal polynomials for measures supported on a finite number of intervals on the real line.
In addition to the Szego and Killip-Simon theorems for orthogonal polynomials on the unit circle (OPUC) and orthogonal polynomials on the real line (OPRL), Simon covers Toda lattices, the moment problem, and Jacobi operators on the Bethe lattice. Recent work on applications of universality of the CD kernel to obtain detailed asymptotics on the fine structure of the zeros is also included. The book places special emphasis on OPRL, which makes it the essential companion volume to the author's earlier books on OPUC.
Titles in the series (2)
- Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space
5
This book is the first to present a new area of mathematical research that combines topology, geometry, and logic. Shmuel Weinberger seeks to explain and illustrate the implications of the general principle, first emphasized by Alex Nabutovsky, that logical complexity engenders geometric complexity. He provides applications to the problem of closed geodesics, the theory of submanifolds, and the structure of the moduli space of isometry classes of Riemannian metrics with curvature bounds on a given manifold. Ultimately, geometric complexity of a moduli space forces functions defined on that space to have many critical points, and new results about the existence of extrema or equilibria follow. The main sort of algorithmic problem that arises is recognition: is the presented object equivalent to some standard one? If it is difficult to determine whether the problem is solvable, then the original object has doppelgängers--that is, other objects that are extremely difficult to distinguish from it. Many new questions emerge about the algorithmic nature of known geometric theorems, about "dichotomy problems," and about the metric entropy of moduli space. Weinberger studies them using tools from group theory, computability, differential geometry, and topology, all of which he explains before use. Since several examples are worked out, the overarching principles are set in a clear relief that goes beyond the details of any one problem.
János Kollár
János Kollár is a professor of Mathematics at Princeton University.
Related to Porter Lectures
Related ebooks
Vincent Price Presents: Tinglers Rating: 0 out of 5 stars0 ratingsFabulous Beekman Boys Present: Polka Spot #3 Rating: 0 out of 5 stars0 ratingsStyx & Stone #2 Rating: 0 out of 5 stars0 ratingsPrimordia Rating: 0 out of 5 stars0 ratingsArt of Mouse Guard Rating: 0 out of 5 stars0 ratingsFlying Saucers Vs. the Earth #4 Rating: 0 out of 5 stars0 ratingsLegend of Isis #10: Volume 2 Rating: 0 out of 5 stars0 ratingsSoma Rating: 0 out of 5 stars0 ratingsNuggets for the Soul: Poems That Will Inspire You Rating: 0 out of 5 stars0 ratingsVincent Price Presents #25 Rating: 0 out of 5 stars0 ratingsMessages from the Heart of Love - Spirituality Basics in 144 Empowering Quotes Rating: 0 out of 5 stars0 ratingsMonster’s Among Us: A War of Witches Rating: 0 out of 5 stars0 ratingsGabriel: The Shattered Star Rating: 0 out of 5 stars0 ratingsJourney to the Moon Rating: 0 out of 5 stars0 ratingsPolitical Power: Michele Bachmann Rating: 0 out of 5 stars0 ratingsOrbit: Mark Zuckerberg, Creator of Facebook Rating: 0 out of 5 stars0 ratingsThe Christmas Fish Rating: 0 out of 5 stars0 ratingsThe Blue Meteor Rating: 0 out of 5 stars0 ratingsFemale Force: Sarah Palin #1 Rating: 0 out of 5 stars0 ratingsIntroductory Business Guide: No Better Time to Start Than Now Rating: 0 out of 5 stars0 ratingsThe Accidental Warriors: The Accidental Warriors, #1 Rating: 0 out of 5 stars0 ratingsRuth & Freddy Rating: 0 out of 5 stars0 ratingsSpecial and Different: The Autistic Traveler: Judgment, Redemption, & Victory Rating: 0 out of 5 stars0 ratingsVincent Price Presents #20 Rating: 0 out of 5 stars0 ratingsBlackbeard Legacy #2 Volume 2 Rating: 0 out of 5 stars0 ratingsBlackbeard Legacy Gallery Rating: 0 out of 5 stars0 ratingsPolitical Power: Rush Limbaugh Rating: 0 out of 5 stars0 ratingsHolding Forth the Word of Life Rating: 0 out of 5 stars0 ratingsSweet Pea Saves the Rainbows Rating: 0 out of 5 stars0 ratings
Mathematics For You
Real Estate by the Numbers: A Complete Reference Guide to Deal Analysis Rating: 0 out of 5 stars0 ratingsThe Thirteen Books of the Elements, Vol. 1 Rating: 0 out of 5 stars0 ratingsMental Math Secrets - How To Be a Human Calculator Rating: 5 out of 5 stars5/5Algebra - The Very Basics Rating: 5 out of 5 stars5/5Standard Deviations: Flawed Assumptions, Tortured Data, and Other Ways to Lie with Statistics Rating: 4 out of 5 stars4/5The Little Book of Mathematical Principles, Theories & Things Rating: 3 out of 5 stars3/5My Best Mathematical and Logic Puzzles Rating: 5 out of 5 stars5/5Quantum Physics for Beginners Rating: 4 out of 5 stars4/5Relativity: The special and the general theory Rating: 5 out of 5 stars5/5Basic Math & Pre-Algebra For Dummies Rating: 4 out of 5 stars4/5The Everything Guide to Algebra: A Step-by-Step Guide to the Basics of Algebra - in Plain English! Rating: 4 out of 5 stars4/5Game Theory: A Simple Introduction Rating: 4 out of 5 stars4/5Calculus Made Easy Rating: 4 out of 5 stars4/5A Mind for Numbers | Summary Rating: 4 out of 5 stars4/5Geometry For Dummies Rating: 5 out of 5 stars5/5ACT Math & Science Prep: Includes 500+ Practice Questions Rating: 3 out of 5 stars3/5Introducing Game Theory: A Graphic Guide Rating: 4 out of 5 stars4/5Algebra I For Dummies Rating: 4 out of 5 stars4/5Limitless Mind: Learn, Lead, and Live Without Barriers Rating: 4 out of 5 stars4/5The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics Rating: 3 out of 5 stars3/5The Everything Everyday Math Book: From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need Rating: 5 out of 5 stars5/5The Math of Life and Death: 7 Mathematical Principles That Shape Our Lives Rating: 4 out of 5 stars4/5Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game - Updated Edition Rating: 4 out of 5 stars4/5Is God a Mathematician? Rating: 4 out of 5 stars4/5Linear Algebra For Dummies Rating: 3 out of 5 stars3/5See Ya Later Calculator: Simple Math Tricks You Can Do in Your Head Rating: 4 out of 5 stars4/5
Related categories
Reviews for Porter Lectures
0 ratings0 reviews