Related papers: The Path to Recent Progress on Small Gaps Between …

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

We show a smoothed version of Goldston-Pintz-Yildirim's sifting argument to detect small gaps between primes, which has a higly flexible error term. Our argument is applicable to high dimensional Selberg sieve situations as well, although…

This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.

This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.

This paper describes the construction of the first explicitly known widely digitally delicate prime.

In the mid-1990s, two groups of authors independently obtained classifications of vertex-transitive graphs whose order is a product of two distinct primes. In the intervening years it has become clear that there is additional information…

Directed graphs can be partitioned in so-called passages. A passage P is a set of edges such that any two edges sharing the same initial vertex or sharing the same terminal vertex are both inside $P$ or are both outside of P. Passages were…

The modern status of large extra dimensional (LED) approaches, highlights of their manifestation and short prehistory are discussed in this paper.

We study small gaps between Goldbach primes $\mathbb{P} \cap (N-\mathbb{P})$ using the Bombieri-Davenport method and the Maynard-Tao method, and compare the two. We show that for almost all even integers $N$, the smallest gap in $\mathbb{P}…

In this brief paper we present some results on creating and manipulating spectral gaps for a (regular) quantum graph by inserting appropriate internal structures into its vertices. Complete proofs and extensions of the results are planned…

This paper reviews recent advances in the field of metallic glasses, focusing on the development of novel experimental techniques and in silico models. We discuss progress in experimental characterization, additive manufacturing, multiscale…

In this paper, we prove a theorem on the distribution of primes in cubic progressions on average.

Some of the most important theoretical and phenomenological aspects of the pinch technique are presented, and several recent developments are briefly reviewed.

Green and Tao proved that the primes contains arbitrarily long arithmetic progressions. We show that, essentially the same proof leads to the following result: The primes in an short interval contains many arithmetic progressions of any…

In this note, we find a new inequality involving primes and deduce several Bonse-type inequalities.

A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright. 3 new formulas are explained.

A quick overview is provided on the current development of the WP metric geometry.

This note discusses the existence of prime numbers in short intervals. An unconditional elementary argument seems to prove the existence of primes in the short intervals [x, x + y], where y >= x^(1/2)(log x)^e, e > 0, and a sufficiently…

In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.

Let $r \ge 2$ be an integer. We adapt the Maynard-Tao sieve to produce the asymptotically best-known bounded gaps between products of $r$ distinct primes. Our result applies to positive-density subsets of the primes that satisfy certain…