It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism […]
The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics. Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example […]
We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions. These Weil […]
Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. […]
Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US […]
The classical Sperner - KKM (Knaster - Kuratowski - Mazurkiewicz) lemma has many applications in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this […]
Abstract: The kissing number problem asks for the maximal number k(n) of equal size nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size. This problem […]
TOPIC: Exploring the fascinating world of prime numbers, Part II The study of patterns in the sequence of prime numbers has fascinated mathematicians for centuries. Are there formulas that generate prime numbers? Are there patterns in the distribution of prime numbers and the distribution of gaps between consecutive primes? In this series of two workshops, […]
I will discuss the concept of transfinite ζ-metrics. In some details I will discuss transfinite Apollonian metric in the settings of semi-metric spaces. I will discuss specific examples of domains where the transfinite Apollonian metric can be computed explicitly. This is a preliminary work.
We begin with a review of the Bateman—Horn conjecture, which sheds light on the intimate relationship between polynomials and prime numbers. In this expository talk, we survey a host of applications of the conjecture. For example, Landau’s conjecture, the twin prime conjecture, and the Green—Tao theorem are all consequences of the Bateman—Horn conjecture. Moreover, the […]
