Related papers: Around Zilber's quasiminimality conjecture

In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.

We provide new formulas for the coefficients in the partial fraction decomposition of the restricted partition generating function. These techniques allow us to partially resolve a recent conjecture of Sills and Zeilberger. We also describe…

We give a new axiomatic treatment of the Zilber trichotomy, and use it to complete the proof of the trichotomy for relics of algebraically closed fields, i.e., reducts of the ACF-induced structure on ACF-definable sets. More precisely, we…

In this paper, we will show that Hausdorff convergence and varifold convergence coincide on the class of almost minimal sets.

A working mathematician's summary of many results on the derived category, perverse sheaves, and vanishing cycles. This is the August 2025 version, with a completely revised section on vanishing cycles.

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

We show that the recently proposed weak gravity conjecture\cite{AMNV0601} can be extended to a class of scalar field theories. Taking gravity into account, we find an upper bound on the gravity interaction strength, expressed in terms of…

This is an expanded version of my plenary lecture at the 8th European Congress of Mathematics in Portoro\v{z} on 23 June 2021. The main part of the paper is a survey of recent applications of complex-analytic techniques to the theory of…

This is lecture notes of a talk I gave at the Morningside Center of Mathematics on June 20, 2006. In this talk, I survey on Poincare and geometrization conjecture.

The purpose of this article is to survey the developments on the Kakeya problem in recent years, concentrating on the period after the excellent 1999 survey of Wolff, and including some recent work by the authors. We will focus on the…

Motivated by Berg's notion of quasi-disjointness for ergodic systems, we introduce and investigate the concept of quasi-disjointness for minimal systems. Several equivalent characterizations are provided. We prove that quasi-disjointness is…

We present a survey of the many and various elements of the modern higher-dimensional theory of quasiconformal mappings and their wide and varied application. It is unified (and limited) by the theme of the author's interests. Thus we will…

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

The document tries to put focus on sequences with certain properties and periods leading to the first value smaller than the starting value in the Collatz problem. With the idea that, if all starting numbers lead ultimately to a smaller…

Let S $\subseteq$ N be a numerical semigroup with multiplicity m, conductor c and minimal generating set P. Let L = S $\cap$ [0, c -- 1] and W(S) = |P||L| -- c. In 1978, Herbert Wilf asked whether W(S) $\ge$ 0 always holds, a question known…

This survey studies pairs $(G,\mathcal{P})$ with $G$ a finitely generated group and $\mathcal{P}$ a (finite) collection of subgroups of $G$. We explore the notion of quasi-isometry of such pairs and the notion of a qi-characteristic…

The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrability, namely integrability close to the boundary, and prove…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

This is an extended abstract of the talk given at the Oberwolfach Workshop "Algebraic Structures in Low-Dimensional Topology", 25 May -- 31 May 2014. My goal was to describe progress in distributive homology from the previous Oberwolfach…

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