Related papers: Multidimensional L2 conjecture: a survey

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 give an elementary proof of the local sum conjecture in two dimensions. In a remarkable paper [CMN, arXiv:1810.11340], this conjecture has been established in all dimensions using sophisticated, powerful techniques from a…

Systematic surveys of astronomical objects often lead to discoveries, but always provide invaluable information for statistical studies of well-defined samples. They also promote follow-up investigations of individual objects or classes.…

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

We survey the state of the union-closed sets conjecture.

In this short survey article, we aim to provide an up to date information on the progress made towards Schurs exponent conjecture and related conjectures. We also mention the connection between Schurs exponent conjecture and Noether's…

This paper contains a detailed, self contained and more streamlined proof of our $l^2$ decoupling theorem for hypersurfaces.

This is a slightly modified version of the survey article. Minor changes to the text and the references have been made.

This is an extended abstract for a survey talk given in Oberwolfach on 1st December 2022, slightly updated in June 2023. I survey some work around the notion of quasiminimality and some of the progress towards Zilber's conjecture from the…

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We give a detailed overview over known results for (no-)collision of a body with the boundary of its container.

L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, the Minkowski sum of two L-convex sets, called L2-convex sets, is an intriguing object that is closely related to polymatroid intersection.…

We survey noncommutative Choquet theory and some of its applications.

This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.

A survey of recent progress in three areas of algebraic combinatorics: (1) the Saturation Conjecture for Littlewood-Richardson coefficients, (2) the n! and (n+1)^{n-1} conjectures, and (3) longest increasing subsequences of permutations.

We survey some recent developments in the analytic theory of multiple Dirichlet series with arithmetical coefficients on the numerators.

In this paper we conjecture a reformulation of the monomial-divisor mirror map for (2,2) mirror symmetry, valid at a boundary of the moduli space, that is easily extended to also include tangent bundle deformations -- an important step…

In this article we survey some of the recent developments in the structure theory of set addition.

This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…

This is a Seminaire Bourbaki survey of the proof of the Kakeya conjecture in three dimensions. The survey is written for a broad mathematical audience. We sketch all the ideas in the proof, with many pictures.