Simon Fraser University

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...

Abstract: Arnold tongues are parameter regions within which dynamics of a mathematical model become mode-locked to a particularfrequency or period. Recent studies of models in a wide variety of fields (examples include models of spiking in neurons, a...

Abstract: In 1992, Thomassen obtained a beautiful proof showing that every planar graphis 5-list-colorable. Some extensions of this result will be presented. Inparticular, a new proof of Thomassen's theorem will be outlined. This proof is...