Related papers: Group Theory in Physics: An Introduction with Math…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
Popular media is an unspoken yet ever-present element of the physics landscape and a tool we can utilize in our teaching. It is also well-understood that students enter the physics classroom with a host of conceptions learned from the world…
The evolution of science education is a dynamic process driven by advances in pedagogy, technology, and especially, our understanding of how students learn. Educators are exploring innovative teaching and learning methodologies such as…
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of this process we propose a principle that generalizations of mathematical structures that are…
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualising more complex principles in group theory. As such they provide an…
I review the basic ingredients of discretized gravity which motivate the introduction of Group Field Theory. Thus I describe the GFT formulation of some models and conclude with a few remarks on the emergence of noncommutative structures in…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
The combination of theory and simulation is necessary in the investigation of properties of complex systems where each method alone cannot do the task properly. Theory needs simulation to test ideas and to check approximations. Simulation…
Infographics are a form of data visualization combining data, information, and statistics. Over the last ten years, infographics have become a popular method for displaying concise information, where infographics are a useful tool for…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Course material for mathematical methods of theoretical physics intended for an undergraduate audience.
Even if students can make the blend, interpret physics correctly in mathematical symbology and graphs, they still need to be able to apply that knowledge in productive and coherent ways. As instructors, we can show our solutions to complex…
These notes provide an opportunity to discover the beauty of Bourbaki set theory, and I hope that they will facilitate the task to those who find it difficult to read this book, one of the most critical elements of the mathematics of…
How far can we take the resource theoretic approach to explore physics? Resource theories like LOCC, reference frames and quantum thermodynamics have proven a powerful tool to study how agents who are subject to certain constraints can act…
In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
Group work is becoming increasingly common in introductory physics classrooms. Understanding how students engage in these group learning environments is important for designing and facilitating productive learning opportunities for…