This is a presentation, along with accompanying commentary, I made on the connexion between harmonic measure and Brownian motion for my Fourier Analysis class.
Through Ito formula and Riesz theorem is shown that the Brownian hitting measure is the harmonic measure.
The hitting measure is shown to corresponds to the Poisson kernel in the upper half-plane, through martingale and uniqueness of Fourier transform.
Here is the latex source of the presentation and the commentary.
I think those files can help someone who does a mathematical talk for the first time. The presentation shows what an effective math slide is, while the commentary shows how to prepare a presentation script.
My talk was 30 minutes long.
The content of those files is also interesting in their own right as they may help to begin in the subject of harmonic measure and Brownian motion.
