The mathematics of Andrei Suslin

Andrei Suslin (1950-2018) was both friend and mentor to us. This article discusses some of his many mathematical achievements, focusing on the role he played in shaping aspects of algebra and algebraic geometry. We mention some of the many important results Andrei proved in his career, proceeding more or less clironolog-ically beginning with Scrre's Conjecture proved by Andrei in 1976 (and simultaneously by Daniel Quillcn). As the reader will quickly ascertain, this article docs not do justice to the many mathematicians who contributed to algebraic K-theory and related subjects in recent decades. In particular, work of Hyman Bass, Alexander BeTlinson, Spencer Bloch, Alexander Grothendieck, Daniel Quillcn. .lean-Pierre Serre, and Christophe Soule strongly influenced Andrei's mathematics and the mathematical developments we discuss. Many important aspects of algebraic /£-theory (e.g., the study of manifolds using surgery and the study of operator algebras) are not mentioned here; such topics are well addressed in various books on algebraic /^-theory such as that of Charles Wcibel.