Geometry at the Quantum Scale

Marcos Duarte Maia was born in the state of North Rio Grande, Brazil. He studied engineering at the State University of Goiás (Brazil), and obtained a BSc degree in Physics in 1966 at the University of Brasilia under supervision of Jayme Tiomno. He moved to London in 1967 to work with Hermann Bondi on gravitational waves as a research student at King's College of the University of London. Soon after, Bondi moved to the ESRO program in Vienna, and his supervision was transferred to Professor Clive  Kilmister. In 1971 he defended a thesis on the subject of Eddington's Fundamental Theory. After his return to Brazil, he was hired by the Department of Mathematics of the University of Brasilia in 1971, where he stayed for the next 20 years, before moving to the Physics Institute of the same university. In 1975, he was a Senior Visitor at the DAMTP, University of Cambridge, in Hawking's group on mini black holes. In the period of 1982 to 1984, he was a an Associate Member visitor to the ICTP (Trieste, Italy) working on the Kaluza-Klein unification program. In 1985 he was a visiting scientist at the University of Washington at Seattle. At the end of his program in Seattle, he moved to the Institute of Theoretical Physics at Santa Barbara, California, and as a research visitor to the Stanford  Linear Accelerator (SLAC). In 1993, he was a Visiting Scientist at the NASA-Fermilab Astrophysical Center near Chicago. His present position is as a Retired Senior Research Associate at the Institute of Physics of the University of Brasilia.

Edmundo Marinho do Monte has a bachelor's degree in mathematics from the Federal University of Paraíba (UFPB), Brazil, a master's degree in atmospheric sciences from UFPB, Brazil, and a PhD in mathematics from the University of Brasília (UnB), Brazil, with a thesis in general relativity. He was a Postdoctoral researcher in relativity at the Department of Geometry and Topology, Granada University (UGR, Spain) and has held visiting professor positions at the International Center for Theoretical Physics (ICTP), Italy, and UGR, Spain. He entered UFPB through competition as a Professor in the Department of Mathematics at UFPB. He is currently Full Professor at the Department of Physics at UFPB, João Pessoa, Brazil. He has experience in the area of physics and mathematics, with an emphasis on fundamental geometric problems in spacetime immersions, working mainly on the following topics: immersions of pseudo-Riemannian manifolds, space-time immersions, geometry and topology of space-times, special and general relativity, cosmology and gravitation.

Chapter 1 A Brief Review on Gauge Forces.- Chapter 2 Gravitation and Cosmology.- Chapter 3 Quantum Gravity.- Chapter 4 Renormalizable Einstein's Gravitation.- Chapter 5 The Renormalizable Einstein's Gravitation.- Chapter 6 Symmetry Mixing.- Chapter 7 The Equations of the Standard Model.- Chapter 8 The Relativistic Poincaré Conjecture.- Chapter 9 The Higgs Roulette.- Chapter 10 Quantum Black Holes at the LHC.