Related papers: Remarks on an interpolation between Wilson's theor…

I settle a conjecture of Andrews related to the Alladi-Schur polynomials. In addition, I give further relations and implications to two families of polynomials related to the Alladi-Schur polynomials.

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

In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…

We prove a result which gives sufficient conditions for a conformal annulus which is a countable union of nested conformal annuli to have bounded modulus. Our theorem also gives estimates for the modulus of such an annulus and is proved…

Paper has been accepted for publication in the Journal f\"ur die reine und Angewandte Mathematik. This version contains the corrections and additional references made in the Galley proofs.

Six conjectures on pairs of consecutive primes are listed in this paper, together with examples for each case.

In this lecture, I put forward conjectures asserting that, in all noncommutative field theories, (1) open Wilson lines and their descendants constitute a complete set of interpolating operators of `noncommutative dipoles', obeying dipole…

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

The Union Closed Sets Conjecture is one of the most renowned problems in combinatorics. Its appeal lies in the simplicity of its statement contrasted with the potential complexity of its resolution. The conjecture posits that, in any union…

For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.

We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.

We present an improved incremental selection algorithm of the selection algorithm presented in [1] and prove all the selected conjectures.

To the best of our knowledge this paper is the first attempt to introduce and study polynomial interpolation of the polynomial data given on arbitrary varieties. In the first part of the paper we present results on the solvability of such…

We study the structure of the Goulden-Jackson-Vakil formula that relates Hurwitz numbers to some conjectural "intersection numbers" on a conjectural family of varieties $X_{g,n}$ of dimension $4g-3+n$. We give explicit formulas for the…

We settled a conjecture of Feigin, Wang and Yoshinaga, appeared in the preprint "Integral expressions for derivations of multiarrangements" (arXiv: 2309.01287v2).

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Padua points is a family of points on the square $[-1,1]^2$ given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The interpolation polynomials and cubature formulas based on the Padua points are…

We give a counterexample to the PIA (precise inversion of adjunction) conjecture for minimal log discrepancies. We also give a counterexample to the LSC conjecture for families.

We give a generalization and a short mechanized proof of determinant conjectured by G. Kuperberg and J. Propp. Further generalizations and applications of the method to some q-analogues may be found in http://www.math.temple.edu/~tewodros

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