Related papers: The Baum-Connes conjecture: an extended survey

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

Recent results about sums of cubes of Fibonacci numbers [Frontczak, 2018] are extended to arbitrary powers.

General considerations on the Equivalence conjectures and a review of few mathematical results.

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…

In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.

An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

Several conjectural continued fractions found with the help of various algorithms are published in this paper.

The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…

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.

Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce…

A survey paper on some recent results on additive problems with prime powers.

We review and provide simplified proofs related to the Magnus expansion, and improve convergence estimates. Observations and improvements concerning the Baker--Campbell--Hausdorff expansion are also made. In this Part IA, we consider…

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.

In this note, we establish the validity of a conjecture recently proposed in Mathematics Magazine and connect it to the existing interesting results

This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct…

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…