Related papers: Chang's Conjectures and Easton collapses
We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…
In this paper, we prove Sp\"ath's Character Triple Conjecture for $p$-solvable groups. This is a conjecture proposed by Sp\"ath during the reduction process of Dade's Projective Conjecture to quasisimple groups. In addition, as suggested by…
This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.
We show that the Coleman-Oort conjecture can be reduced to three particular cases. As an application we extend a result of Lu and Zuo, to the effect that for g at least 8 the Coleman-Oort conjecture is true on the hyperelliptic locus.
We obtain average results on the Sato-Tate conjecture for elliptic curves for small angles.
Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We propose a simple model which possesses the chain fountain effect.
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…
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
Answering a question of Sakai, we show that the existence of an $\omega_1$-Erd\H{o}s cardinal suffices to obtain the consistency of Chang's Conjecture with $\square_{\omega_1, 2}$. By a result of Donder this is best possible. We also give…
We give two simple proofs of a conjecture of Richard Stanley concerning the equidistribution of derangements and alternating permutations with the maximal number of fixed points.
We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his…
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hoped that the ideas introduced here may lead to further…
In this paper, we give a simple counter example to the famous Hodge conjecture.
In the present note, we give a short proof of Brennan's conjecture in the special case of continuous semigroups of holomorphic functions. We apply classical techniques of complex analysis in conjunction with recent results on…
In this paper, we prove a conjecture of Schnell in the surface case.
We prove Simon's conjecture for 3-manifolds.
The well-known 1-2-3 Conjecture asserts that the edges of every graph without isolated edges can be weighted with $1$, $2$ and $3$ so that adjacent vertices receive distinct weighted degrees. This is open in general, while it is known to be…