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The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by “standard monomials”. In its modern form, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.

Mathematics. --- Algebraic geometry. --- Algebra. --- Field theory (Physics). --- Algebraic Geometry. --- Field Theory and Polynomials. --- Classical field theory --- Continuum physics --- Algebraic geometry --- Math --- Geometry, algebraic. --- Physics --- Continuum mechanics --- Geometry --- Polynomials. --- Mathematics --- Mathematical analysis

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The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series. The aim of this course was to give an introduction to the series of papers by concentrating on the case of the full linear group. In recent years, there has been great progress in standard monomial theory due to the work of Peter Littelmann. The author’s lectures (reproduced in this book) remain an excellent introduction to standard monomial theory. d-origin: initial; background-clip: initial; background-position: initial; background-repeat: initial;">Standard monomial theory deals with the construction of nice bases of finite dimensional irreducible representations of semi-simple algebraic groups or, in geometric terms, nice bases of coordinate rings of flag varieties (and their Schubert subvarieties) associated with these groups. Besides its intrinsic interest, standard monomial theory has applications to the study of the geometry of Schubert varieties. Standard monomial theory has its origin in the work of Hodge, giving bases of the coordinate rings of the Grassmannian and its Schubert subvarieties by “standard monomials”. In its modern form, standard monomial theory was developed by the author in a series of papers written in collaboration with V. Lakshmibai and C. Musili. In the second edition of the book, conjectures of a standard monomial theory for a general semi-simple (simply-connected) algebraic group, due to Lakshmibai, have been added as an appendix, and the bibliography has been revised.

Algebra --- Geometry --- Mathematics --- Classical mechanics. Field theory --- algebra --- landmeetkunde --- wiskunde --- fysica --- mechanica

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Islamic literature, Turkish --- History and criticism --- Turkey --- Intellectual life --- Intellectual life. --- Islamic literature, Turkish. --- Turkey.

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The ICM 2010 satellite conference 'Geometry, Topology and Dynamics in Negative Curvature' afforded an excellent opportunity to discuss various aspects of this fascinating interdisciplinary subject in which methods and techniques from geometry, topology, and dynamics often interact in novel and interesting ways. Containing ten survey articles written by some of the leading experts in the field, this proceedings volume provides an overview of important recent developments relating to negative curvature. Topics covered include homogeneous dynamics, harmonic manifolds, the Atiyah Conjecture, counting circles and arcs, and hyperbolic buildings. Each author pays particular attention to the expository aspects, making the book particularly useful for graduate students and mathematicians interested in transitioning from other areas via the common theme of negative curvature.

Curvature. --- Integral geometry. --- Geometry, Integral --- Geometry, Differential --- Calculus --- Curves --- Surfaces

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The chapters presented in this book ‘Biofortification of Food Crops’ depict how agricultural technological interventions have true role in alleviating malnutrition. This book highlights the role of multidisciplinary approaches to cope up with the challenges of micronutrient malnutrition or hidden hunger which is an alarming public health issue in most parts of the world including India. In this endeavour, different biofortification approaches such as agronomic (or ferti-fortification), breeding, biotechnological, physiological, microbial etc. has fulfilled their different mandates of nutrient enrichment of food crops including cereals and pulses. The contents of the book proves that biofortified plants have adequate potential to nourish nutrient depleted soils, help increase crop productivity and provide nutritional benefits to plants, humans and livestock. The content and quality of information presented in this book will definitely provide multiple novel ideas of advance techniques and will stimulate innovative thoughts and directions amongst researchers and policy makers in the field of biofortification. In addition, the contributions presented in the book will be a good source of background knowledge and technical know-how to educate the readers about biofortification. The authors hope that the book entitled “Biofortification of Food Crops” would provide a suitable platform in our collective efforts for an appropriate dialogue among the scientists, researchers, entrepreneurs, policy makers and farmers in reducing the budding issues of malnutrition through novel approaches and means.

Biomedical Engineering --- Health & Biological Sciences --- Food crops. --- Food crops --- Biotechnology. --- Food --- Plants, Edible --- Field crops --- Horticultural crops --- Food science. --- Nutrition. --- Botany. --- Agriculture. --- Food Science. --- Plant Sciences. --- Public Health. --- Farming --- Husbandry --- Industrial arts --- Life sciences --- Food supply --- Land use, Rural --- Botanical science --- Phytobiology --- Phytography --- Phytology --- Plant biology --- Plant science --- Biology --- Natural history --- Plants --- Alimentation --- Nutrition --- Health --- Physiology --- Diet --- Dietetics --- Digestion --- Food habits --- Malnutrition --- Science --- Health aspects --- Food—Biotechnology. --- Nutrition   . --- Plant science. --- Public health. --- Community health --- Health services --- Hygiene, Public --- Hygiene, Social --- Public health services --- Public hygiene --- Social hygiene --- Human services --- Biosecurity --- Health literacy --- Medicine, Preventive --- National health services --- Sanitation --- Floristic botany