Wadim ZudilinAffiliation: University of Newcastle, Australia Email: Wadim.Zudilin@newcastle.edu.au Title Of Talk: On certain irrational values of the logarithm: beyond the 1979 limitations Abstract: In a note ``On certain irrational values of the logarithm" by Alladi and Robinson, a family of integrals was introduced to investigate the irrationality of logarithms of some (simple) algebraic numbers. (The integrals were inspired by Beukers' proof of Ap\'ery's theorem about the irrationality of $\zeta(2)$ and $\zeta(3)$.) The note concluded with a discussion of natural limitations of the method, for example, its failure to approach the irrationality of $\log(3)$ and $\pi$. In my talk I will explain how the Alladi--Robinson integrals, without any modification, are used in establishing that the latter two numbers are irrational.
Title of Special Colloquium: Short random walks and Mahler measures An $n$-step uniform random walk is a walk that starts at the origin and consists of $n$ steps of length 1 each taken into a uniformly random direction. It is particularly interesting for $n=2,3,4,5$ because of its beautiful links to modular and hypergeometric functions. The Mahler measure of an $n$-variable polynomial is its geometric mean over the $n$-dimensional torus. There are several cases when $n$-variate Mahler measures are known or conjectured to be linked to hypergeometric functions and noncritical $L$-values, for small $n$ as well. In the talk I will outline the links above and indicate some new interconnections between the short random walks and Mahler measures. These novel results are from joint work in progress with Armin Straub. WARNING: This page contains MATH-JAX
Last update made Tue Mar 1 07:24:54 PST 2016.
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