PrerequisiteMeasure Theory, Probability (Martingales)AbstractLaplacian growth is the study of interfaces that move in proportion to harmonic measure. We survey progress over the last decade on discrete models of (internal) Laplacian growth, including the abelian sandpile, internal DLA (first analyzed by Lawler, Bramson and Griffeath in 1992), rotor aggregation, and the scaling limits of these m...
IntroductionThe notion of height was invented by André Weil to prove the famous Mordell's conjecture (if A is an abelian variety defined over a number field K, then A(K) is a finitely generated abelian group). In this class, we will study some properties of the logarithmic, absolute Weil height. We will also discuss about open problems related to this useful tool. At the end, we will construct ...