Related papers: Dialogues about geometry and light
This text is a short but comprehensive introduction to the basics of supergeometry and includes some of the recent advances in colored supergeometry. We do not aim for a standard text that states results and proves them more or less…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
From a modern perspective cosmology is a historical science in so far that it deals with the development of the universe since its origin some 14 billion years ago. The origin itself may not be subject to scientific analysis and…
Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
There is a contemporary trend toward geometrizing all mathematical theories, as proposed by the Langlands program, and, by extension, physical theories as well. Within this paradigm, it becomes possible to represent physical objects as…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
In classical geometry, there is no such well-known and much-studied topic as the construction of conic sections (or briefly conics) from its five points. Its importance in many applications of mechanical engineering, civil engineering and…
Light microscopy allows observing cellular features and objects with sub-micrometer resolution. As such, light microscopy has been playing a fundamental role in the life sciences for more than a hundred years. Fueled by the availability of…
These lecture notes (from the Second Autumn School in High Energy Physics and Quantum Field Theory, Yerevan 2014) cover a number of topics related to geometric quantization. Most of the material is presented from a physicist's point of…
I present a simple view of nonlinear optcal phenomena as being determined mostly by the length of interaction time between photons and matter. This may explain why in the last decades the progress in developing better nonlinear materials…
Strong lensing is a powerful tool to address three major astrophysical issues: understanding the spatial distribution of mass at kpc and sub-kpc scale, where baryons and dark matter interact to shape galaxies as we see them; determining the…
Mathematics is one of the ways our species makes sense of this world and I believe that it is inherent in our thinking machinery. The mathematics we do in turn is dependent on the way we view our universe and ourselves. Lakoff and Nunez…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
Starting from classical algebraic geometry over the complex numbers (as it can be found for example in Griffiths and Harris it was the goal of these lectures to introduce some concepts of the modern point of view in algebraic geometry. Of…
The learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which…
Quantum optics potentially offers an information channel from the Universe beyond the established ones of imaging and spectroscopy. All existing cameras and all spectrometers measure aspects of the first-order spatial and/or temporal…
Intense light-matter interaction largely relies on the use of high-power light sources, creating fields comparable to, or even stronger than, the field keeping the electrons bound in atoms. Under such conditions, the interaction induces…
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the…