Related papers: Multidimensional L2 conjecture: a survey
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…
This is a survey on Kawaguchi-Silverman conjecture.
We survey recent developments on the Restriction conjecture.
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
We present a history of the Baum-Connes conjecture, the methods involved, the current status, and the mathematics it generated.
This is a survey paper of the developments on the geometric Bogomolov conjecture. We explain the recent results by the author as well as previous works concerning the conjecture. This paper also includes an introduction to the height theory…
This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…
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.
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
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.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
This is a non-technical survey of a recent theory of valuations on manifolds constructed in math.MG/0503397, math.MG/0503399, math.MG/0509512, math.MG/0511171 and actually a guide to this series of articles. We review also some recent…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
The purpose of this survey is to present the recent advances about the Pollicott-Ruelle resonances.
The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson…
This survey is an invitation to recent developments in higher dimensional birational geometry.
This is a survey on recent results on the Loewner theory in one and several complex manifolds
We discuss various recent advances on weak forms of the Twin Prime Conjecture.
We survey recent developments towards a proof of the Penrose conjecture and results on Penrose-type and other geometric inequalities for quasi-local masses in general relativity.