Related papers: The Eisenbud-Green-Harris Conjecture
This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
New cases of the multiplicity conjecture are considered.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
In this paper we present the statement of the Firoozbakht's conjecture, some of its consequences if it is proved and we show a consequence of Zhang's theorem concerning the Firoozbakht's conjecture.
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
We prove the Strengthened Hanna Neumann Conjecture, in its common graph theoretic formulation. Our original approach to this conjecture used cohomology of sheaves on graphs, although here we give a short combinatorial proof that we found in…
We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].
An overview of last seven years results concerning Sarnak's conjecture on M\"obius disjointness is presented, focusing on ergodic theory aspects of the conjecture.
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].
We survey three results on syzygies of curves beyond Green's conjecture, with a particular emphasis on drawing connections between the study of syzygies and other topics in moduli theory.
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
The Union Closed Sets Conjecture states that in every finite, nontrivial set family closed under taking unions there is an element contained in at least half of all the sets of the family. We investigate two new directions with respect to…
In this paper the circulant Hadamard conjecture is proved.
In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.