Infosheet (November 7th, 2017) |
Queen's University - Department of Mathematics and Statistics |
Wednesday, November 8 |
Number Theory Seminar Time: 1:30 p.m. Place: Jeffery 319 |
Speaker: Francesco Cellarosi Title: Smooth Sums over Smooth k-Free Integers Abstract Attached |
Friday, November 10 |
Remembrance Day Services Time: 10:30 a.m. Place: Grant Hall |
Classes cancelled 10:30 am – 11:30 am |
Friday, November 10 |
Department Colloquium Time: 2:30 p.m. Place: Jeffery 234 |
Speaker: Hector Pasten, Harvard University Title: In Quest of Arithmetic Derivatives Abstract Attached |
Friday, November 24 |
Ph.D. Thesis Defense Time: 10:00 a.m. Place: Jeffery 521 |
Ph.D. Student: Aaron Springford Title: Spectral analysis of time series with latent and irregular times Supervisors: D. Thomson and G. Takahara |
Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.
Wednesday, November 8, 1:30 p.m. Jeffery 319 - Number Theory Seminar
Speaker: Francesco Cellarosi
Title: Smooth Sums over Smooth k-Free Integers
Abstract: We provide an asymptotic estimate for certain sums over k-free integers with small prime factors. These sums depend upon a complex parameter $\alpha$ and involve a smooth cut-off $f$. They are a variation of several classical number-theoretical sums. One term in the asymptotics is an integral operator whose kernel is the $\alpha$-convolution of the Dickman-de Bruijn distribution, and the other term is explicitly estimated. The trade-off between the value of $\alpha$ and the regularity of $f$ is discussed.
Friday, November 10, 2:30 p.m. Jeffery 234 - Department Colloquium
Speaker: Hector Pasten
Title: In Quest of Arithmetic Derivatives
Abstract: There are well-known arithmetic analogies between integers and polynomials (or more generally, holomorphic functions), specially with respect to solutions of Diophantine equations. A crucial aspect that is missing in this analogy is that for polynomials and holomorphic functions one can use derivatives, while for integers there is no direct substitute of this operation. After some motivation, I will discuss a couple of possible candidates for arithmetic derivatives.