Geometry, Algebra and Applications: From Mechanics to Cryptography

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Marco Castrillón López, Luis Hernández Encinas, Pedro Martínez Gadea, Ma Eugenia Rosado María
Springer, Jun 30, 2016 - Science - 198 pages

This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.

 

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Contents

A Survey on Homogeneous Structures on the Classical Hyperbolic Spaces
1
On the 1+3 Threading of Spacetime
13
Local Structure of SelfDual Gradient Yamabe Solitons
25
The Prescribed Curvature Problem in Low Dimension
36
EulerPoincaré Reduction by a Subgroup of Symmetries as an Optimal Control Problem
49
Morse Families and Lagrangian Submanifolds
65
Properties and Applications
79
Rotation Minimizing Vector Fields and Frames in Riemannian Manifolds
91
Classes of Nonlinear Filters for Stream Ciphers
107
Implementation of Cryptographic Algorithms for Elliptic Curves
120
Supermanifolds Symplectic Geometry and Curvature
135
Prime Submodules and Symmetric Algebras
147
Application to Cybersecurity of the Stability Theory of the Systems of Ordinary Differential Equations
157
On the Nontriviality of the EightForm τ4ω on Manifolds with a Spin9Structure
170
Flaws in the Application of Number Theory in Key Distribution Schemes for Multicast Networks
181
EinsteinHilbert Lagrangian Induced on the Linear Frame Bundle
188

Local Anomaly Cancellation and Equivariant Cohomology of Jet Bundles
101

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About the author (2016)

Prof. Marco Castrillón López read Mathematics and Physics in Madrid. He is currently Profesor Titular at the Universidad Complutense de Madrid, where he also received his Ph.D. in Mathematics. He was a postdoc at École Polytechnique Fédérale de Lausanne (Switzerland), and Faculty Visitor at Caltech (Pasadena, USA), PIMS (Vancouver, Canada), Imperial College (London, UK), TATA Institute (Mumbay, India) and PUC (Rio de Janeiro, Brazil). His research work mainly focuses on geometric variational calculus, gauge theories and Riemannian geometry with applications to relativity, classical field theories and other topics in theoretical physics. His has over 50 publications and books to his name.

Prof. Pedro M. Gadea taught at the Universities of Santiago de Compostela and Valladolid in Spain. He is now a scientific researcher at the Instituto de Física Fundamental, CSIC, Madrid, Spain. He has published almost seventy research papers on several topics of differential geometry and algebraic topology. He has also been the advisor for four Ph.D. theses. His current interests are Differential Geometry, more specifically in homogeneous spin Riemannian manifolds and Ricci-flat invariant Kähler structures.

L. Hernández Encinas graduated in Mathematics at the University of Salamanca (Spain) in 1980, and received his Ph.D. in Mathematics at the same university in 1992. He is a researcher at the Department of Information Processing and Cryptography (TIC) at the Institute of Physical and Information Technologies (ITEFI), Spanish National Research Council (CSIC) in Madrid. He has participated in more than 30 research projects. He is author of 9 books, 9 patents, more than 150 papers, and over 100 contributions to workshops and conferences. He has also supervised several doctoral theses. His current research interests include cryptography and cryptanalysis of public key cryptosystems, digital signature schemes, authentication and identification protocols, crypto-biometry, side channel attacks, and number theory problems.

M. Eugenia Rosado María graduated in Mathematics at the University Complutense de Madrid, and obtained her Ph.D. in Mathematics at the same university. She taught at the Universities Autónoma de Madrid, Spain and currently teaches at the Universidad Politécnica de Madrid. She has published around 20 papers on several topics in differential geometry. Her research interests are in geometrical variational calculus, geometric methods in differential equations, differential invariants and other topics in differential geometry.