Related papers: Perfectoid Spaces: A survey
We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao.
A perfect cuboid is a rectangular parallelepiped whose edges, whose face diagonals, and whose space diagonal are of integer lengths. The problem of finding such cuboids or proving their non-existence is not solved thus far. The second…
One of the most stimulating recent ideas in particle physics involves a possibility that our universe has additional compactified spatial dimensions, perhaps as large as 1 mm. In this review, we discuss the results of recent experimental…
The present talk summarizes the recently progressed state of a systematic re-evaluation of cosmological models that respect the presence of inhomogeneities. Emphasis is given to identifying the basic steps towards an effective (i.e.…
This paper is an introduction and a survey to the concept of perfect isometries which was first introduced by Michel Brou{\'e} in 1990. Our main aim is to provide proofs of numerous results scattered in the literature. On the other hand, we…
The most celebrated aspects of precision physics are briefly summarized. New ideas are also introduced that may lead to further developments in the field of radiative corrections, with special emphasis to multi-loop numerical evaluation and…
In this note we introduce generalised pairs from the perspective of the evolution of the notion of space in birational algebraic geometry. We describe some applications of generalised pairs in recent years and then mention a few open…
The theoretical expectations for the supersymmetric particle spectrum is reviewed and a brief overview on present constraints on supersymmetric models from collider experiments is presented. Finally, we discuss the discovery potential of…
I was asked at the end of this conference to provide a few comments on the present status of the field of cosmic abundances, which I summarize (and extend upon) in this contribution. A discussion of the present ``state of play'' is given,…
This paper presents an extended version of lecture notes for an introductory course on Berkovich analytic spaces that I gave in 2010 at Summer School "Berkovich spaces" at Institut de Mathmatiques de Jussieu.
Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined…
A survey paper on some recent results on additive problems with prime powers.
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
In this paper, we introduce round and sleek topological spaces and study their properties.
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
In this semi-expository paper we review the notion of a spherical space. In particular we present some recent results of Wedhorn on the classification of spherical spaces over arbitrary fields. As an application, we introduce and classify…
In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.
Lattice results in supersymmetry are summarized. Past, present and future perspectives are discussed.