Related papers: Some recent progress on the Restriction conjecture

The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…

A conjecture regarding the structure of expander graphs is discussed.

We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

Some observations on the Wu-Sprung potential.

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

We summarize recent progress in describing the confinement-deconfinement transition from a novel perturbative approach.

We survey some recent development in the stability theory of klt singularities. The main focus is on the solution of the stable degeneration conjecture.

These lecture notes describe the current state of affairs for Manin's conjecture in the context of del Pezzo surfaces.

In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…

This paper describes some of the ideas used in the development of our work on small gaps between primes.

We review the progress made at LEP in the quest for new particles.

This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.

One of the great endeavors of the past decade has been the evaluation of different observational techniques for measuring dark energy properties and of theoretical techniques for constraining models of cosmic acceleration given cosmological…

This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.

We consider the swampland distance and de Sitter conjectures, of respective order one parameters $\lambda$ and $c$. Inspired by the recent Trans-Planckian Censorship conjecture (TCC), we propose a generalization of the distance conjecture,…

An updated review is presented of lattice investigations of colour confinement.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

We give a proof of some small weight and level cases of Serre's conjecture.

This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.