Explore the intriguing world of number theory in this 1-hour 7-minute lecture from the Colloque des sciences mathématiques du Québec. Delve into the divisor function, which calculates the number of positive divisors for natural numbers. Investigate strategies for comprehending this function's behavior across the natural number spectrum, examining distribution patterns and their implications. Discover fascinating connections between the divisor function, the Riemann zeta function, and random matrix groups. Gain insights into advanced mathematical concepts as presented by Matilde Lalín from the Université de Montréal, offering a deeper understanding of number theory and its intersections with other mathematical domains.