Michael Levitin – författare

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.|This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Seminaire de Mathematiques Superieures on Geometric and Computational Spectral Theory, held from June 15-26, 2015, at the Centre de Recherches Mathematiques, Universite de Montreal, Montreal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.

It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question ``Can one hear the shape of a drum?'' In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

The fight for a $15 minimum wage. Nationwide teacher strikes. Bernie Sanders’s political revolution and the rise of AOC. Black Lives Matter. #MeToo. Read how the Occupy movement helped reshape American politics, culture and the groundbreaking movements to follow. On the ten-year anniversary of the Occupy movement, Generation Occupy sets the historical record straight about the movement’s lasting impacts. Far from a passing phenomenon, Occupy Wall Street marked a new era of social and political transformation, reigniting the labor movement, remaking the Democratic Party and reviving a culture of protest that has put the fight for social, economic, environmental and racial justice at the forefront of a generation. The movement changed the way Americans see themselves and their role in the economy through the language of the 99 versus the 1 percent. But beyond that, in its demands for fairness and equality, Occupy reinvigorated grassroots activism, inaugurating a decade of youth-led resistance movements that have altered the social fabric, from Black Lives Matter and Standing Rock to March for Our Lives, the Global Climate Strikes and #MeToo. Bookended by the 2008 financial crisis and the coronavirus pandemic, Generation Occupy attempts to help us understand how we got to where we are today and how to draw on lessons from Occupy in the future.