Related papers: A Counter Example To the Hodge Conjecture
This is a short note on the log canonical inversion of adjunction.
We survey some old and new results on strong variants of Chang's Conjecture and related topics.
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, "Note on the uniqueness of the solution of an equation of interest in inverse scattering problem", J. Math.Phys., 11, N3, (1970), 815-817.
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…
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline…
We look at an old conjecture of A. Tarski on cardinal arithmetic and show that if a counterexample exists, then there exists one of length omega_1 + omega .
This is a survey on Sarnak's Conjecture
In this paper, besides a counterexample to Bloch's principle, normality criteria leading to counterexamples to the converse of Bloch's principle in several complex variables are proved. Some Picard-type theorems and their corresponding…
Suppose that Y is a cyclic cover of projective space branched over a hyperplane arrangement D, and that U is the complement of the ramification locus in Y. The first theorem implies that the Beilinson-Hodge conjecture holds for U if certain…
We prove several extensions of the Erdos-Fuchs theorem.
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.
Error in proof of theorem 10.
In this short paper we will show, via elementary arguments, the equivalence of the Twin Prime Conjecture to a problem which might be simpler to prove. Some conclusions are drawn, and it is shown that proving the Twin Prime Conjecture is…
We describe a new source of counterexamples to the so-called integral Hodge and integral Tate conjectures. As in the other known counterexamples to the integral Tate conjecture over finite fields, ours are approximations of the classifying…
We propose a simple model which possesses the chain fountain effect.
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.
The purpose of the paper is to present an short proof of the Chuang's inequality.