Simon Fraser University

Abstract: Self assembly is the idea of creating a system whose component parts spontaneously assemble into a structure of interest. In biological systems, there are striking examples where complicated structures (ie the bacterial ribosome) can...

There is a marked difference in the weather patterns and climate between the Earth's equatorial and midlatitude regions. Much of this difference is due to the active role of moisture and convection in the tropics. However, the even the dry fluid...

AbstractIn modern language, Fermat's Descent Infini establishes that an elliptic curve has a Mordell-Weil group of rank 0. Since then, the method has been generalized to provide an upper bound on the rank of any elliptic curve and further work also...

Abstract. In recent past we were interested to study some special composition of polynomial equation f(g(x)) = f(x)hm(x) where f, g and h are unknown polynomials with coefficients in arbitrary field K, f is non-constant and separable, deg g ! 2, g! "...

AbstractMany arithmetic geometric results have an arithmetic dynamic analogue. For instance, Siegel's theorem that an elliptic curve has only finitely many integer points is analogous to the fact that any orbit under a rational function whose second...

AbstractWe summarize the current meager state of knowledge concerning how often values of polynomials have only small prime factors (that is, the values are "friable" or "smooth"). We also present some evidence, in the form of a theorem conditional...

Abstract We will present new conjectures on polynomial equations with constant coefficients over a function field of arbitrary characteristic (joint work with Ghioca). These statements are inspired by previous conjectures from Zilber, Pink and...

Abstract We consider a system of k diagonal polynomials of degrees 1, 2,..., k. Using methods developed by W.T. Gowers and refined by Green and Tao to obtain bounds in the 4-term case of Szemeredi's Theorem on long arithmetic progressions, we show...

Abstract: Representations of the Galois group of the rationals abound in nature and are important in understanding the structure of the Galois group of the rational numbers. Iwasawa theory studies certain arithmetic modules arising from such...

Abstract: In early 1960's, Lang proved that if for a given polynomial G(X,Y) with complex coefficients, there exist infinitely many pairs (x,y) where both x and y are roots of unity such that G(x,y) = 0, then essentially G(X,Y) = X^mY^n - c, for some...