相关论文: Notes on the Milnor conjectures

We give new proofs on Arnold Chord Conjecture and Weinstein Conjecture in M\times C which generalizes the previous works.

We give the counter-examples related to a Gaussian Brunn-Minkowski inequality and the (B) conjecture.

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

We give an introduction to unstable motivic homotopy theory of Morel and Voevodsky, and survey some results.

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

Proofs of results due to Johansson, \"Oberg and Pollicott are given which correct some aspects of the originals. This leads to modifications to the most general results; however, the main corollaries are unaffected.

This paper presents the best known bounds for a conjecture of Gluck and a conjecture of Navarro.

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

We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…

We propose several Hodge theoretic analogues of the conjectures of Hopf and Singer, and prove them in some special cases.

The paper presents a counterexample to the Hodge conjecture.

These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…

The Milnor conjecture has been a driving force in the theory of quadratic forms over fields, guiding the development of the theory of cohomological invariants, ushering in the theory of motivic cohomology, and touching on questions ranging…

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

In the paper, the authors provide four alternative proofs of an explicit formula for computing Bernoulli numbers in terms of Stirling numbers of the second kind.

Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

This note is the follow up to a paper by M. Waldschmidt.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

We establish the second part of Milnor's conjecture on the volume of simplexes in hyperbolic and spherical spaces. A characterization of the closure of the space of the angle Gram matrices of simplexes is also obtained.