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A simplified view of the space of optimised stellarators has the potential to guide and aid the design efforts of magnetic confinement configurations suitable for future fusion reactors. We present one such view for the class of…
The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete…
This set of lecture notes first gives an introduction to the geometry of principal bundles. Next, it demonstrates how they can be used to formalize the concept of gauge theories arising in physics. A basic familiarity with the differential…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
We introduce an axiomatic theory of spherical diagrams as a tool to study certain combinatorial properties of polyhedra in $\mathbb R^3$, which are of central interest in the context of Art Gallery problems for polyhedra and other…
Applications of decision diagrams in quantum circuit analysis have been an active research area. Our work introduces FeynmanDD, a new method utilizing standard and multi-terminal decision diagrams for quantum circuit simulation and…
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
Let $M$ be a subset of vector space or projective space. The authors define the \emph{generalized configuration space} of $M$ which is formed by $n$-tuples of elements of $M$ where any $k$ elements of each $n$-tuple are linearly…
We present a method for a recursive graphical construction of Feynman diagrams with their correct multiplicities in quantum electrodynamics. The method is first applied to find all diagrams contributing to the vacuum energy from which all…
We study the construction of local subtraction schemes through the lenses of tropical geometry. We focus on individual Feynman integrals in parametric presentation, and think of them as particular instances of Euler integrals. We provide a…
In this paper, we propose a design methodology for one-class classifiers using an ensemble-of-classifiers approach. The objective is to select the best structures created during the training phase using an ensemble of spanning trees. It…
This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation…
In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models.…
Bottom-up layout algorithms for compound graphs are suitable for presenting the microscale view of models and are often used in model-driven engineering. However, they have difficulties at the macroscale where maintaining the overview of…
We review the hypergeometric function approach to Feynman diagrams. Special consideration is given to the construction of the Laurent expansion. As an illustration, we describe a collection of physically important one-loop vertex diagrams…
Wiring diagrams usually serve as a tool in the study of arrangements of lines and pseudolines. In this paper we go in the opposite direction, using known properties of line arrangements to motivate certain equivalence relations and actions…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
We show that observables in QED-type theories can be realized in terms of a combinatorial structure called chord diagrams. One advantage of this combinatorial representation is that it simplifies the study of the asymptotic behavior of…
`Categorification' is the process of replacing equations by isomorphisms. We describe some of the ways a thoroughgoing emphasis on categorification can simplify and unify mathematics. We begin with elementary arithmetic, where the category…
We propose a generalization of the classical point-line Cremona-Richmond configuration to a configuration of points and more dimensional subspaces of a projective space, and present them as geometric realizations of some interesting…