Related papers: Recent advances on Kawaguchi-Silverman conjecture
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.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
Some topics from recent progresses in lattice QCD are reviewed.
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…
The main purpose of the following article is to give a proof of Y. Kawamata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an $\displaystyle L^{2\over…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
This document collects several approaches attempted in proving the Chen-Raspaud Conjecture for k = 3. Each approach is detailed with full proofs and explanations of why it failed. This compilation aims to provide insights and a foundation…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.
A survey of some recent advances in parabolic Hitchin systems (parabolic Bouville--Narasimhan--Ramanan correspondence, mirror symmetry for parabolic Hitchin systems), and in exact methods of solving the non-parabolic Hitchin systems.
This is a detailed survey on the QWEP conjecture and Connes' embedding problem. Most of contents are taken from Kirchberg's paper [Invent. Math. 112 (1993)].
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
This paper gives a survey of the progress on the minimal genus problem since Lawson's survey.
We describe recent advances in the study of random analogues of combinatorial theorems.
We provide new sufficient conditions under which Ryser's conjecture holds.
General considerations on the Equivalence conjectures and a review of few mathematical results.
Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.
This is a survey paper on Geometric Manin's conjecture which was proposed by Brian Lehmann and the author. We introduce Geometric Manin's conjecture (GMC) and review some recent progress on this conjecture.
In this paper we prove the WALA conjecture.