Title: Concentrations and singularities in PDEs

Abstract: One of the milestones of the structure theory for functions of bounded variation (BV functions) is Alberti’s Rank One Theorem. This theorem describes how the polar of the singular part of the gradient of a BV function is constrained to have rank one almost everywhere. I will put this result into the broader context of concentration in PDEs and present a recent work of mine (joint with Filip Rindler from Warwick) where we resolved the Vanishing Mass Conjecture. I will try to connect this result with previous works in the field and show some of its consequences.