Gaussian Multiplicative Chaos on balls: Laplace transforms, small deviations and some connections with maximal packing

During my talk i will show some new representations of Laplace transforms of the Gaussian Multiplicative Chaos (GMC) on Euclidean balls in R^d. I will discuss the problem of small deviations of GMC and their lognormal asymptotic bounds. I will also present some ideas how to use GMC in the problem of maximal packing. Based on two separte works: one with Anna Talarczyk-Noble and second with Jacek Jakubowski.