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This article surveys recent advances and future challenges in the $2$-representation theory of finitary $2$-categories with a particular emphasis on problems related to classification of various classes of $2$-representations.
We briefly outline the present state of the $n\bar{n}$ transition problem and compare two alternative models.
In this contribution, I review some of the latest advances in calculational techniques in theoretical particle physics. I focus, in particular, on their application to the calculation of highly non-trivial scattering processes, which are…
We discuss the issues surrounding the implementation of quantum computation in rare-earth-ion doped solids. We describe a practical scheme for two qubit gate operations which utilise experimentally available interactions between the qubits.…
We study effects of the physical realization of quantum computers on their logical operation. Through simulation of physical models of quantum computer hardware, we analyse the difficulties that are encountered in programming physical…
An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…
I review the status of the comparisons between a few measurements at hadronic colliders and perturbative QCD predictions, which emphasize the need for improving the current computations. Such improvements will be mandatory for a…
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.
Numerical Relativity is concerned with solving the Einstein equations, as well as any field or matter equations on curved space-time, by means of computer calculations. The methods developed for this purpose up to now, as well as the…
An overview of quantum computing and in particular the Hidden Subgroup Problem are presented from a mathematical viewpoint. Detailed proofs are supplied for many important results from the literature, and notation is unified, making it…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
Computational complexity is a core theory of computer science, which dictates the degree of difficulty of computation. There are many problems with high complexity that we have to deal, which is especially true for AI. This raises a big…
We report the first steps in creating an optical computing system. This system may solve NP-Hard problems by utilizing a setup of exponential sized masks. This is exponential space complexity but the production of those masks is done with a…
The demands of cutting-edge science are driving the need for larger and faster computing resources. With the rapidly growing scale of computing systems and the prospect of technologically disruptive architectures to meet these needs,…
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer…
Modeling hydrological fracture networks is a hallmark challenge in computational earth sciences. Accurately predicting critical features of fracture systems, e.g. percolation, can require solving large linear systems far beyond current or…
In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…
This lecture addresses some general ideas behind numerical computations ranging from representation of numbers in computers to stability and accuracy of standard algorithms for some simple mathematical problems.
We give a brief account of the current limitations and possibilities in the field of computational simulation of materials. We then focus on the effect that the emergence of machine learning interatomic potentials is having on the field and…