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Author: Fritz Gesztesy
Publisher: Springer
ISBN: 3319299778
Category : Mathematics
Languages : en
Pages : 191
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Book Description
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.
Author: Fritz Gesztesy
Publisher: Springer
ISBN: 3319299778
Category : Mathematics
Languages : en
Pages : 191
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Book Description
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.
Author: Nora Doll
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3111173089
Category : Mathematics
Languages : en
Pages : 590
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Book Description
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.
Author: Felix L. Schwenninger
Publisher: Springer Nature
ISBN: 3031649915
Category :
Languages : en
Pages : 262
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Book Description
Author: Thomas Piketty
Publisher: Harvard University Press
ISBN: 0674979850
Category : Business & Economics
Languages : en
Pages : 817
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Book Description
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.
Author: Peter Marcuse
Publisher: Verso Books
ISBN: 1804294942
Category : Political Science
Languages : en
Pages : 257
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Book Description
In every major city in the world there is a housing crisis. How did this happen and what can we do about it? Everyone needs and deserves housing. But today our homes are being transformed into commodities, making the inequalities of the city ever more acute. Profit has become more important than social need. The poor are forced to pay more for worse housing. Communities are faced with the violence of displacement and gentrification. And the benefits of decent housing are only available for those who can afford it. In Defense of Housing is the definitive statement on this crisis from leading urban planner Peter Marcuse and sociologist David Madden. They look at the causes and consequences of the housing problem and detail the need for progressive alternatives. The housing crisis cannot be solved by minor policy shifts, they argue. Rather, the housing crisis has deep political and economic roots—and therefore requires a radical response.
Author: David Easley
Publisher: Cambridge University Press
ISBN: 1139490303
Category : Computers
Languages : en
Pages : 745
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Book Description
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.
Author: Dmitri Rabounski
Publisher: Infinite Study
ISBN:
Category :
Languages : en
Pages : 72
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Book Description
The Journal on Advanced Studies in Theoretical and Experimental Physics, including Related Themes from Mathematics
Author: Eugenia Cheng
Publisher: Profile Books
ISBN: 1782830812
Category : Mathematics
Languages : en
Pages : 191
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Book Description
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.
Author: Steven C. Ferry
Publisher: Cambridge University Press
ISBN: 0521497965
Category : Mathematics
Languages : en
Pages : 386
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Book Description
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'.
Author: Gérard Genette
Publisher: Cornell University Press
ISBN: 9780801492594
Category : Language Arts & Disciplines
Languages : en
Pages : 292
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Book Description
Genette uses Proust's Remembrance of Things Past as a work to identify and name the basic constituents and techniques of narrative. Genette illustrates the examples by referring to other literary works. His systemic theory of narrative deals with the structure of fiction, including fictional devices that go unnoticed and whose implications fulfill the Western narrative tradition.
