Theoretical Statistics and Mathematics Unit, ISI 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.