Related papers: Multidimensional L2 conjecture: a survey

In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.

I give a brief overview of the status of lattice QCD, concentrating on topics relevant to phenomenology. I discuss the calculation of the light quark spectrum, the lattice prediction of $\alpha_\MS(M_Z)$, and the calculation of $f_B$.

I review recent progress in defining a probability measure in the inflationary multiverse. General requirements for a satisfactory measure are formulated and recent proposals for the measure are clarified and discussed.

This paper takes a new step in the direction of proving the Duffin-Schaeffer Conjecture for measures arbitrarily close to Lebesgue. The main result is that under a mild `extra divergence' hypothesis, the conjecture is true.

In this paper we survey many of the known results about Morse boundaries and stability.

Inference and prediction are fundamental to the study of complex systems, where network data are often incomplete, inaccurate or obtained indirectly. In this paper, we review recent advances in network sampling and comparison, as well as in…

The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.

Submanifold theory is a very active vast research field which plays an important role in the development of modern differential geometry. This branch of differential geometry is still so far from being exhausted; only a small portion of an…

We establish an expansion theory for $\text{SL}_2(\mathbb Z/q\mathbb Z)$. Incorporating this into a framework recently developed by Shkredov, we confirm Zaremba's conjecture.

This article gives a brief overview of the status of attempts to constrain inflation using observations, and examines prospects for future developments.

This is a survey paper about a selection of results in complex algebraic geometry that appeared in the recent and less recent litterature, and in which rational homogeneous spaces play a prominent r{\^o}le. This selection is largely…

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

In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.

These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform,…

This is a survey paper concerning some theorems on stochastic convex ordering and their applications to functional inequalities for convex functions. We present the recent results on those subjects

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

We develop the $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular $L$-functions using multiple Dirichlet series under the generalized Riemann…

In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.

This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…

In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic…