Related papers: On Arnold's and Pushkin's puzzles
We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold's strange…
In this essay dedicated to Yakov Eliashberg we survey the current state of the field of Lagrangian (un)knots, reviewing some constructions and obstructions along with a number of unsolved questions. The appendix by Georgios Dimitroglou…
It is shown that Darwiche and Pearl's postulates imply an interesting property, not noticed by the authors.
We give a survey of some recent papers by the authors and Masaaki Wada relating the twisted Alexander polynomial with a partial order on the set of prime knots. We also give examples and pose open problems.
We prove some extensions of Andrews inequality.
Problems in optimization and geometric probability are discussed, all connected with angles subtended at an observer's eye by an object at a distance. Several of these remain unsolved.
A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.
We give a geometric approach to the relation between the irreducible components of the characteristic varieties of local systems on a plane curve arrangement complement and the associated pencils of plane curves discovered recently by M.…
A conjecture of I. Krasikov is proved. Several discrete analogues of classical polynomial inequalities are derived, along with results which allow extensions to a class of transcendental entire functions in the Laguerre-P\'olya class.
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
Two letters from William Burnside have recently been found in the Nachlass of Robert Fricke that contain instances of Burnside's Problem prior to its first publication. We present these letters as a whole to the public for the first time.…
Using Pustejovsky's "The Syntax of Event Structure" and Fong's "On Mending a Torn Dress" we give a glimpse of a Pustejovsky-like analysis to some example sentences in Fong. We attempt to give a framework for semantics to the noun phrases…
We explore an (unpublished) approach to the famous Jacobian Conjecture by means of identities of algebras, discovered by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951{2001). This approach also indicates some…
These notes discuss in an informal manner the construction and some properties of 1- and 2-gerbes. They are mainly based on the author's previous work in this area, which is reviewed here, and to some extent improved upon. The main emphasis…
We survey the classical results of the Dirichlet Approximation Theorem.
This note is an addendum to [1,2], pointing out the differences between these papers and raising open questions.
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
I present a set of remarks related to joint works \cite{paper1},\cite{paper2},\cite{paper3},\cite{MMNO}. These are remarks about polynomials solutions and vertex operators, eigenproblem for polynomials and a remark related to the the…
We describe a relation between Arnold's strange duality and a polar duality between the Newton polytopes which is mostly due to M.~Kobayashi. We show that this relation continues to hold for the extension of Arnold's strange duality found…
This article covers my second talk at the Gathering for Gardner in March, 2010. It is about an Odd One Out puzzle I invented, after having been inspired by Martin Gardner. I do not like Odd One Out questions; that is why I invented one.