Geometry, Algebra and Applications: From Mechanics to Cryptography

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

Prof. Pedro M. Gadea taught at the Universities ofSantiago de Compostela and Valladolid in Spain. He is now a scientificresearcher at the Instituto de Física Fundamental, CSIC, Madrid, Spain. He has publishedalmost seventy research papers on several topics of differential geometry and algebraictopology. He has also been the advisor for four Ph.D. theses. His currentinterests are Differential Geometry, more specifically in homogeneous spinRiemannian 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 aresearcher at the Department of Information Processing and Cryptography (TIC)at the Institute of Physical and Information Technologies (ITEFI), SpanishNational Research Council (CSIC) in Madrid. He has participated in more than 30research projects. He is author of 9 books, 9 patents, more than 150 papers, andover 100 contributions to workshops and conferences. He has also supervised severaldoctoral theses. His current research interests includecryptography and cryptanalysis of public key cryptosystems, digital signature schemes,authentication and identificationprotocols, crypto-biometry, side channelattacks, and number theory problems.

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

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

1 W. Batat, P. M. Gadea, J. A. Oubiña, A survey on homogeneousstructures on the classical hyperbolic spaces.- 2 A. Bejancu, On the (1 + 3) threading of spacetime.- 3 M. Brozos-Vázquez, E.Calviño-Louzao, E. García-Río, R. Vázquez-Lorenzo, Local structure ofself-dual gradient Yamabe solitons.- 4 G. Calvaruso, The prescribed curvature problem in low dimension.-5 M.Castrillón López, P. L. García, Euler-Poincare reduction by a subgroup ofsymmetries as an optimal control problem.- 6 M. Castrillón López, T. S. Ratiu, Morse families andLagrangian submanifolds.- 7 R. Durán Díaz, L. Hernández Encinas, Special primes: properties and applications.-8 F. Etayo, Rotation Minimizing vectorfields and frames in Riemannian manifolds.- 9 R. Ferreiro Pérez, Local anomaly cancellation and equivariantcohomology of jet bundles.- 10 A. Fúster-Sabater, F. Montoya Vitini, Classes of nonlinear filters for streamciphers.- 11 V. Gayoso Martínez, L. Hernández Encinas, A.Martín Muñoz, Implementation of cryptographic algorithms for ellipticcurves.- 12 R.Hernández-Amador, J. Monterde, J. Vallejo, Supermanifolds, symplectic geometry and curvature.-13 A. Marcelo, F. Marcelo, C. Rodríguez, Prime submodules and symmetric algebras.- 14 A. Martín del Rey, G. Rodríguez Sánchez, Application to cybersecurityof the stability theory of the systems of ordinary differential equations.- 15I. V. Mykytyuk, On the non-triviality of the eight-form T4(w) on manifolds with a Spin(9)-structure.- 16 A. Peinado, Flaws in the applicationof Number Theory in Key Distribution Schemes for Multicast Networks.- 17 L. Pozo, E. Rosado, Einstein-HilbertLagrangian induced on the linear frame bundle.