Graduate Student Paper Session

Saturday Morning

UC 106

8:00 – 8:15 The Dynamics of Maps of the Torus
Sebastian Mineo, Fairfield University

Abstract: In this paper, we begin with a brief discussion of the chaotic nature of hyperbolic automorphisms onto the torus. We then continue by classifying all two-dimensional non-hyperbolic toral automorphisms up to topological conjugacy using purely elementary means. Finally, we investigate the dynamics of these maps and discuss the possibility for chaos.

8:20 – 8:35 Hyperelliptic Curves in Characteristic Two
Yasin Demirbas, Boston University

Abstract: Hyperelliptic Curves are a special class of algebraic curves and can be viewed as generalizations of elliptic curves. Starting in 1989, the theory of hyperelliptic curves over finite fields has been applied to construction of cryptosystems. The attack by Duursma-Gaudry-Morain is feasible if the Jacobian has an automorphism of large order, and to protect against the attack by Gaudry, the genus g of the hyperelliptic curve must be smaller than 5. So, one needs to know the automorphism groups as well. In this talk we will give a complete list of the automorphism groups of hyperelliptic curves of genus 3, and 4 over an algebraically closed field of characteristic 2.

8:40 – 8:55 The Bochner Identity in Euclidean Space
Zachary J. Smith, University of Maine – Orono

Abstract : The Fourier transform is a useful technique in looking at solutions to partial differential equations. In its study, we try to gain understanding by decomposing it into functions that remain invariant under symmetries. We shall achieve this by looking at eigenfunctions of the Laplace-Beltrami operator, resulting in some nice relations involving Bessel functions.