The Mathematical Heritage of Alexander Grothendieck
From 1955 to about 1970 Alexander Grothendieck (1922-2014) initiated a revolutionary period in the field of algebraic geometry. I would like to describe his general intellectual style and explain why his work was so influential. I will focus on the early period: his work on homological algebra and sheaf theory, the foundations of algebraic geometry, and his proof of the general Riemann-Roch theorem. If time permits I will explain his approach to the Weil conjectures. I hope that large parts of this will be accessible to students.