Texas A&M Number Theory Seminar

Department of Mathematics
Milner 216
Thursdays, 1:00-2:00 PM

Title: Duality in diophantine approximation

Abstract: We describe three kinds of duality: the first one rests on Khinchine transference principle, and has been used recently by Damien Roy in a question of simultaneous diophantine approximation; the second one is related to Fourier-Borel transform and deals with exponential polynomials. The third one is useful for computing the height of certain matrices related with quantitative refinements of Hermite-Lindemann Theorem on the transcendence of the exponential of an algebraic number.

Title: Transcendental numbers: history and development

Abstract: The theory starts in 1844 with Lindemann, we describe the early stages in XIXth century, the main developments in the XXth century and we conclude with open problems.

Title: Multiple zeta values

Abstract: The values of Riemann's zeta function at positive integers had been studied already by Euler. In his investigation of products of such values he introduced multiple zeta values, namely

sum_{n_1 > n_2 > ... > n_k}    n_1^{-s_1}\cdots n_k^{-s_k}

when s_1, ..., s_k are positive integers with n_1 >= 2. These numbers are related by a number of algebraic relations which give rise to a rich algebraic structure. The main open problem is to prove that all such relations are the known ones.