相关论文: The artinian conjecture (following Djament, Putman…

In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.

This is a Bourbaki report on the work of Y. Andr\'e on the direct summand conjecture, and subsequent developments by Andr\'e and Bhatt on big Cohen-Macaulay algebras.

The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).

This note is an exposition of the proof of Thom's conjecture by Kronheimer and Mrowka, using the new Seiberg-Witten invariants.

In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].

This is the text of my Bourbaki seminar on the proof of the surface subgroup conjecture by Jeremy Kahn and Vladimir Markovic.

Recently, Straub gave an interesting $q$-analogue of a binomial congruence of Ljunggren. In this note we give an inductive proof of his result.

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

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

We provide a proof of the Borwein Conjecture using analytic methods.

Dumont has conjectured a marvellous identity, which generalizes, in particular, the classical results of Lagrange, Gauss, Jacobi and Kronecker on the sums of two, three and four squares. We give a combinatorial proof of Dumont's conjecture.

We give a simplified exposition of the easiest case of a breakthrough result by D.Badziahin, A.Pollington and S.Velani related to W.M.Schmidt's conjecture.

The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize…

This note is based on the original proof of the shuffle conjecture by Carlsson and Mellit (arXiv:1508.06239, version 2), which seems to be too concise for the combinatorial community. James Haglund spent a semester to check through the…

We give a new proof of a_4\phi_3 summation due to G.E. Andrews and confirm another_4\phi_3 summation conjectured by him recently. Some variations of these two_4\phi_3 summations are also given.

This is a survey on Sarnak's Conjecture

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

We settle in the affirmative the Graham-Sloane conjecture.

The article provides a counterexample to a conjecture by Blocki-Zwonek.

We prove a conjecture of Rudnick and Sarnak on the mass equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxiv.org:math/0809.1635.