Dr. Alessandro Carbotti “A quantitative dimension free isoperimetric inequality for the fractional Gaussian perimeter”

We prove a quantitative isoperimetric inequality for the fractional Gaussian perimeter using extension techniques. Though the exponent of the Fraenkel asymmetry is not sharp, the constant appearing in the inequality does not depend on the dimension but only on the Gaussian volume of the set and on the fractional order. In the last part of the talk we give a brief overview on open problems and possible generalizations.