Related papers: Open problems on polynomials, their zero distribut…
Open problems of the conference "Automorphisms of Affine Spaces" held July 6-10 2009 at the Radboud University, Nijmegen, The Netherlands.
This paper has been submitted to the Proceedings of the Australian-German Workshop on Differential Geometry in the Large held at the mathematical research institute MATRIX in Creswick, Victoria, Australia, Feb.2-Feb.14, 2019. We describe…
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and…
We prove some new results about the spacing between neighboring zeros of paraorthogonal polynomials on the unit circle. Our methods also provide new proofs of some existing results. The main tool we will use is a formula for the phase of…
Volume with the Late-Breaking Abstracts submitted to the Evo* 2023 Conference, held in Brno (Czech Republic), from 12 to 14 of April. These papers present ongoing research and preliminary results investigating on the application of…
The conference `Geometric and Asymptotic Group Theory with Applications (GAGTA) 2023: Groups and Dynamics' took place at the Erwin Schr\"odinger Institute on July 17-21. These are the problems that were proposed during the Problem Session:…
In this paper we investigate the distribution of zeros of Boubaker polynomials.
Lecture given at BW2003 Workshop "Mathematical, Theoretical and Phenomenological Challenges Beyond Standard Model" 29 August-02 September, 2003 Vrnjacka Banja, Serbia
These are the notes of my lectures at the 1996 European Congress of Mathematicians. {} Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones.…
This short note serves as a historical introduction to the Hopf problem: "Does there exist a complex structure on $S^6$?" This unsolved mathematical question was the subject of the Conference "MAM 1 $-$ (Non-)Existence of Complex Structures…
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes of a tutorial I gave at the NATO Advanced Study Institute on…
We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The…
This is the list of open problems in topological algebra posed on the conference dedicated to the 20th anniversary of the Chair of Algebra and Topology of Lviv National University, that was held on 28 September 2001.
A fast and weakly stable method for computing the zeros of a particular class of hypergeometric polynomials is presented. The studied hypergeometric polynomials satisfy a higher order differential equation and generalize Laguerre…
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…
The subject of Polynomiography deals with algorithmic visualization of polynomial equations, having many applications in STEM and art, see [Kal04]. Here we consider the polynomiography of the partial sums of the exponential series. While…
In this note, we provide a wide range of upper bounds for the moduli of the zeros of a complex polynomial. The obtained bounds complete a series of previous papers on the location of zeros of polynomials.
These are extended notes for my lectures at the workshop ``Reconstructing the Gravitational Hologram'' held at Galileo-Galilei Institute, Florence, in June 2022.
We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some well-known families of polynomials, and the interplay between these models and the asymptotic distribution of their…