By Yuri Tschinkel,Yuri Zarhin
invited expository and study articles on new advancements bobbing up from
Manin’s striking contributions to mathematics.
Read or Download Algebra, Arithmetic, and Geometry: Volume II: In Honor of Yu. I. Manin: 270 (Progress in Mathematics) PDF
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The purpose of this ebook is to provide the elemental innovations and houses of the geodesic circulation of a closed Riemannian manifold. the themes lined are on the subject of my examine pursuits. a huge aim here's to explain homes of the geodesic circulation which don't require curvature assumptions. a regular instance of one of these estate and a significant bring about this paintings is Mane's formulation that relates the topological entropy of the geodesic circulation with the exponential progress price of the typical numbers of geodesic arcs among issues within the manifold.
In line with a two-semester path aimed toward illustrating a variety of interactions of 'pure arithmetic' with different sciences, akin to hydrodynamics, thermodynamics, statistical physics and data idea, this article unifies 3 basic subject matters of research and physics, that are as follows: the dimensional research of actual amounts, which includes numerous functions together with Kolmogorov's version for turbulence; features of very huge variety of variables and the main of focus besides the non-linear legislation of enormous numbers, the geometric that means of the Gauss and Maxwell distributions, and the Kotelnikov-Shannon theorem; and, ultimately, classical thermodynamics and get in touch with geometry, which covers major ideas of thermodynamics within the language of differential types, touch distributions, the Frobenius theorem and the Carnot-Caratheodory metric.
This is often the 1st booklet on a newly rising box of discrete differential geometry delivering an exceptional technique to entry this interesting region. It presents discrete equivalents of the geometric notions and techniques of differential geometry, corresponding to notions of curvature and integrability for polyhedral surfaces.
Eine verständlich und konzis geschriebene Einführung in die Algebra, die durch ihre sorgfältige didaktische Aufbereitung besticht. Die 7. Auflage bietet neben zahlreichen Aufgaben (mit Lösungshinweisen) sowie einführenden Vorbemerkungen auch Ausblicke auf neuere Entwicklungen. Der Autor spricht selten behandelte Themen wie Resultanten und Witt-Vektoren an.
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Additional info for Algebra, Arithmetic, and Geometry: Volume II: In Honor of Yu. I. Manin: 270 (Progress in Mathematics)
Algebra, Arithmetic, and Geometry: Volume II: In Honor of Yu. I. Manin: 270 (Progress in Mathematics) by Yuri Tschinkel,Yuri Zarhin