Related papers: A note on the Artin Conjecture

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We prove that the Center Conjecture passes to the Artin groups whose defining graphs are cones, if the conjecture holds for the Artin group defined on the set of the cone points. In particular, it holds for every Artin group whose defining…

We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two…

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

An asymptotic formula for the number of integers with the primitive root 2, and a generalized Artin primitive root conjecture for composite integers is presented here.

This is a survey on Sarnak's Conjecture

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.

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.

In this paper, we will continue the investigation of Waring's problem, and give further improvements.

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…

We discuss some aspects of the theory of subelliptic estimates.

In this paper, we prove a conjecture of Schnell in the surface case.

The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.

This is a brief survey of recent results related to austere submanifolds, mainly based on the papers [24,25].

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.

This note provides a self-contained exposition of the proof of the artinian conjecture, following closely Djament's Bourbaki lecture. The original proof is due to Putman, Sam, and Snowden.

In this article, we give a proof on the Arnold-Chekanov Lagrangian intersection conjecture on the cotangent bundles and its generalizations.

In this paper the circulant Hadamard conjecture is proved.