Title: Acute triangulations of convex polytopes

Abstract: Acute triangulation in the plane is a subdivision into acute triangles. Similarly, an acute triangulation in higher dimensions is a subdivision into simplices with acute dihedral angles. The problem of finding acute triangulations is a classical problem in discrete geometry motivated by applications to the finite element method. In the last few years there have been several breakthroughs, both positive (possibility results in low dimensions) and negative (impossibility of acute triangulations in higher dimensions). We we will survey the literature and close with open problems. The talk will be completely accessible to the general audience and hopefully somewhat entertaining.