Geometric phenomena can often be expressed in terms of inequalities that relate certain quantities in an optimal way. Fundamental such examples include the isoperimetric inequality and the Brunn-Minkowski inequality. This workshop brings together promising junior researchers and leading experts in the field to discuss recent breakthroughs related to such geometric inequalities, both in the context of differential and convex geometry. A designated goal of this workshop is to explore possible synergies between these two areas that will ideally lead to new collaborations between the participants.