In this talk, we will discuss two significant strengthenings of this result (one due to myself and I. Łaba, another due to myself, G. Kiss, I. Łaba and G. Somlai), which are derived from complexity measurements for polynomials with integer coefficients which have many cyclotomic polynomial divisors. As applications, we give connections in two other areas of mathematics. The first is in the study of integer tilings: additive decompositions of the integers Z = A+B as a sum set, where each integer is represented uniquely. The second application is to the Favard length problem in fractal geometry, which asks for bounds upon the average length of the projections of certain dynamically-defined fractals onto lines.
This talk is based upon my individual work, as well as my joint work with I. Łaba, as well as my joint work with G. Kiss, I. Łaba and G. Somlai. All are welcome, and the first 15-20 minutes will include introductory ideas and examples for all results discussed in the latter portion of the talk.
Contact:
Cherie Secrist | cherie.secrist@uleth.ca | (403) 329-2470