Gregory L. Naber

TL;DR: Classical, Conformal and Topological Field Theory Classical Mechanics Condensed Matter Physics and Optics Differential Geometry Dirac Operators Dynamical Systems Fluid Dynamics Functional Analysis and Variational Techniques Gauge Theory General Relativity Integrable Systems Lie Groups and Lie Algebras Many Particle Systems Noncommutative Geometry Partial Differential Equations and ODEs Path Integrals and Functional Integrals Perturbation Theory Quantization Techniques Quantum Field Theory Quantum Gravity Quantum Groups Quantum Information and Computation Quantum Mechanics Renormalization Scattering Theory Semi-classical App

TL;DR: In this paper, physical and geometrical motivation for topological spaces, principal bundles, differentiable manifolds, and matrix Lie groups are discussed, as well as manifold fields and instantons.

TL;DR: In this paper, the authors present a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics, including a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, and a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group.

TL;DR: Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer fixed point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem and the Lefschetz Fixed Point Theorem are discussed in this paper.