Rigid Spindle Sander

Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study "nth order linear differential equations by studying the rank "n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1, infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard "nth order generalizations of the hypergeometric function, n"Fn-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the "l-adic Fourier Transform.

This book provides the first unified examination of the relationship between Radon transforms on symmetric spaces of compact type and the infinitesimal versions of two fundamental rigidity problems in Riemannian geometry. Its primary focus is the spectral rigidity problem: Can the metric of a given Riemannian symmetric space of compact type be characterized by means of the spectrum of its Laplacian? It also addresses a question rooted in the Blaschke problem: Is a Riemannian metric on a projective space whose geodesics are all closed and of the same length isometric to the canonical metric? The authors comprehensively treat the results concerning Radon transforms and the infinitesimal versions of these two problems. Their main result implies that most Grassmannians are spectrally rigid to the first order. This is particularly important, for there are still few isospectrality results for positively curved spaces and these are the first such results for symmetric spaces of compact type of rank >1. The authors exploit the theory of overdetermined partial differential equations and harmonic analysis on symmetric spaces to provide criteria for infinitesimal rigidity that apply to a large class of spaces. A substantial amount of basic material about Riemannian geometry, symmetric spaces, and Radon transforms is included in a clear and elegant presentation that will be useful to researchers and advanced students in differential geometry.

Jil Sander - Jil Sander, born Heidemarie Jiline Sander in Wesselburen near Hamburg (Germany) on 27 November 1943, is a German fashion designer known for minimalist designs and her perfume line. It is also the name of the fashion house she founded, Jil Sander AG.

Spindle Galaxy in Draco - The Spindle Galaxy in Draco (also known as the Spindle Galaxy, Lenticular Galaxy NGC 5866 or NGC 5866) is a lenticular galaxy, type S0_3, in the Draco constellation. Astronomers believe that the Spindle Galaxy may be the same as Messier Object 102.

Spindle checkpoint - The spindle checkpoint blocks the entry of a cell undergoing mitosis into anaphase until all chromosomes are properly attached to the meiotic or mitotic spindle. To achieve proper segregation, the two kinetochores on the sister chromatids must be attached to opposite spindle poles.

Spindle neuron - Spindle neurons are a specific class of neurons that participate in signal transmission in the nervous system, and are characterized by a large spindle shaped soma, gradually tapering into a single apical dendrite (axon) in one direction, with only a single dendrite facing opposite. Whereas other types of neurons tend to have many dendrites, the polar shaped morphology of spindle neurons is unique, having only been found in two very restricted regions in the brains of hominids - the family of species ...

rigidspindlesander

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