Dr. Jonathan L. ALPERIN

ALPERIN, Dr. Jonathan L. "Jon" Age 88, of Chicago, IL, passed away peacefully on June 22, 2025, in Chicago. He was born to Jordan and Esther Alperin in Boston, Massachusetts. He was preceded in death by his parents; and his younger brother, Jeremy. Jon is survived by his nephew, Greg; and his niece, Courtney. A constant throughout Jon's life was his love of the Boston Red Sox, travel, nice meals accompanied by great wine, classical music, long walks through the English countryside, and mathematics.

Jon had a profound impact on the study of finite groups throughout his long career, uncovering phenomena at levels both broadly general and sharply technical. His 1961 doctoral dissertation from Princeton University, entitled "On a Special Class of Regular p-groups," marked the beginning of an interest in groups of prime power order that would last over thirty years and culminate in a collaboration with his colleague, George Glauberman, establishing an existence criteria for such groups to have abelian normal subgroups of prescribed size.

But certainly, Jon's best-known work lies at the opposite end of the spectrum in that it is an indispensable tool in the understanding of simple groups. This is the Alperin Fusion Theorem, the main result of his 1967 paper "Sylow intersections and fusion," which makes precise the sense in which conjugation can always be understood locally and allows for a unified treatment of several nonsimplicity criteria.

Jon also contributed directly to the classification of finite simple groups in his collaboration with Daniel Gorenstein and Richard Brauer. The three published a major work in 1970 that, in particular, determined the finite simple groups whose Sylow 2-subgroups are quasi-dihedral. From there, Jon took an interest in the modular representation theory and cohomology of finite groups, giving a novel approach to Brauer's First Main Theorem and several elegant applications of the Green Correspondence. The most widely recognized achievement from this era is his 1979 paper with Michel Broué, "Local methods in block theory" in which they establish a Sylow theory for blocks. Jon's later book, Local Representation Theory, continues to be widely cited.

At the 1986 Arcata Conference on Representations of Finite Groups in Arcata, California, Jon announced what is now known as Alperin's Weight Conjecture, identifying a simple way in which the number of irreducible representations of a finite group in positive characteristic is determined locally. Many consider this to be one of the major currently outstanding problems in the theory of finite groups.

But of course, Jon's research legacy is and must be more than a list of static results. It is a way of thinking, an attitude, an eye for elegance, and a refined intuition. Twenty-three people completed doctoral degrees under his supervision.

He will be missed.