The Callias Index Formula Revisited

The Callias Index Formula Revisited
Author: Fritz Gesztesy
Publisher: Springer
Total Pages: 191
Release: 2016-06-28
Genre: Mathematics
ISBN: 3319299778

These lecture notes aim at providing a purely analytical and accessible proof of the Callias index formula. In various branches of mathematics (particularly, linear and nonlinear partial differential operators, singular integral operators, etc.) and theoretical physics (e.g., nonrelativistic and relativistic quantum mechanics, condensed matter physics, and quantum field theory), there is much interest in computing Fredholm indices of certain linear partial differential operators. In the late 1970’s, Constantine Callias found a formula for the Fredholm index of a particular first-order differential operator (intimately connected to a supersymmetric Dirac-type operator) additively perturbed by a potential, shedding additional light on the Fedosov-Hörmander Index Theorem. As a byproduct of our proof we also offer a glimpse at special non-Fredholm situations employing a generalized Witten index.

Spectral Flow

Spectral Flow
Author: Nora Doll
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 590
Release: 2023-06-19
Genre: Mathematics
ISBN: 3111173089

This is the first treatment entirely dedicated to an analytic study of spectral flow for paths of selfadjoint Fredholm operators, possibly unbounded or understood in a semifinite sense. The importance of spectral flow for homotopy and index theory is discussed in detail. Applications concern eta-invariants, the Bott-Maslov and Conley-Zehnder indices, Sturm-Liouville oscillation theory, the spectral localizer and bifurcation theory.

Capital in the Twenty-First Century

Capital in the Twenty-First Century
Author: Thomas Piketty
Publisher: Harvard University Press
Total Pages: 817
Release: 2017-08-14
Genre: Business & Economics
ISBN: 0674979850

What are the grand dynamics that drive the accumulation and distribution of capital? Questions about the long-term evolution of inequality, the concentration of wealth, and the prospects for economic growth lie at the heart of political economy. But satisfactory answers have been hard to find for lack of adequate data and clear guiding theories. In this work the author analyzes a unique collection of data from twenty countries, ranging as far back as the eighteenth century, to uncover key economic and social patterns. His findings transform debate and set the agenda for the next generation of thought about wealth and inequality. He shows that modern economic growth and the diffusion of knowledge have allowed us to avoid inequalities on the apocalyptic scale predicted by Karl Marx. But we have not modified the deep structures of capital and inequality as much as we thought in the optimistic decades following World War II. The main driver of inequality--the tendency of returns on capital to exceed the rate of economic growth--today threatens to generate extreme inequalities that stir discontent and undermine democratic values if political action is not taken. But economic trends are not acts of God. Political action has curbed dangerous inequalities in the past, the author says, and may do so again. This original work reorients our understanding of economic history and confronts us with sobering lessons for today.

Networks, Crowds, and Markets

Networks, Crowds, and Markets
Author: David Easley
Publisher: Cambridge University Press
Total Pages: 745
Release: 2010-07-19
Genre: Computers
ISBN: 1139490303

Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others.

Beyond Infinity

Beyond Infinity
Author: Eugenia Cheng
Publisher: Profile Books
Total Pages: 191
Release: 2017-03-09
Genre: Mathematics
ISBN: 1782830812

SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1

Novikov Conjectures, Index Theorems, and Rigidity: Volume 1
Author: Steven C. Ferry
Publisher: Cambridge University Press
Total Pages: 386
Release: 1995-11-23
Genre: Mathematics
ISBN: 0521497965

These volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'.

Progress in Physics, vol. 4/2016

Progress in Physics, vol. 4/2016
Author: Dmitri Rabounski
Publisher: Infinite Study
Total Pages: 72
Release:
Genre:
ISBN:

The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics

Luxury Arts of the Renaissance

Luxury Arts of the Renaissance
Author: Marina Belozerskaya
Publisher: Getty Publications
Total Pages: 292
Release: 2005-10-01
Genre: Art
ISBN: 0892367857

Today we associate the Renaissance with painting, sculpture, and architecture—the “major” arts. Yet contemporaries often held the “minor” arts—gem-studded goldwork, richly embellished armor, splendid tapestries and embroideries, music, and ephemeral multi-media spectacles—in much higher esteem. Isabella d’Este, Marchesa of Mantua, was typical of the Italian nobility: she bequeathed to her children precious stone vases mounted in gold, engraved gems, ivories, and antique bronzes and marbles; her favorite ladies-in-waiting, by contrast, received mere paintings. Renaissance patrons and observers extolled finely wrought luxury artifacts for their exquisite craftsmanship and the symbolic capital of their components; paintings and sculptures in modest materials, although discussed by some literati, were of lesser consequence. This book endeavors to return to the mainstream material long marginalized as a result of historical and ideological biases of the intervening centuries. The author analyzes how luxury arts went from being lofty markers of ascendancy and discernment in the Renaissance to being dismissed as “decorative” or “minor” arts—extravagant trinkets of the rich unworthy of the status of Art. Then, by re-examining the objects themselves and their uses in their day, she shows how sumptuous creations constructed the world and taste of Renaissance women and men.