# Seminar at SMU Delhi

September 26, 2018 (Wednesday) , 3:30 PM at Webinar
Speaker: Rahul Roy, ISI Delhi
Title: Two applications of probability in analysis
Abstract of Talk
Ever since Kakutani showed that the Dirichlet problem is intricately connected with the Brownian motion, many questions of analysis have been solved by probabilistic methods. In this talk we discuss two such questions. In the first part we discuss the Poisson equation $\frac{1}{2} \bigtriangleup u = -1 \mbox{ on a domain } D \subset \mathbb R^d$ with boundary conditions $u = 0 \mbox{ on } \delta D.$ We obtain an explicit solution for this problem when $D$ is an equilateral triangle. Next we provide a probabilistic proof of the Euler's formula $\zeta(2) = \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}$, where $\zeta$ is the Riemann's zeta function.