Talk #1
Jérémy Champagne, Department of Pure Mathematics, University of Waterloo
"Diophantine approximation by linear forms with angular restrictions"
We are interested by generalisations of Dirichlet’s theorem on approximation by linear forms. Following the work of Schmidt, we look at the case where some proportions are imposed on the coefficient of the linear forms. For example, some may want to look at linear forms with strictly positive coefficients, or at linear forms where the first coefficient is the largest in absolute value. In a joint paper with Damien Roy, we give a systematic way to establish the best exponent of approximation in that case. In this talk, I will cover some elements of the proof, which are mainly due to Schmidt and Thurnheer.
Talk #2
Yu-Ru Liu, Department of Pure Mathematics, University of Waterloo
"Equidistribution of Polynomial Sequences in Function Fields"
We prove a function field analog of Weyl's equidistribution theorem of polynomial sequences. Our result covers the case when the degree of the polynomial is greater than or equal to the characteristic of the field, which is a natural barrier when applying the Weyl differencing process to function fields. This is joint work with Thài Hoàng Lê and Trevor D. Wooley.
MC 5417