## Richard Block Lecture Series

### Richard Block

#### Current Talk 03/02/2017:

#### Background on the Richard E. Block Distinguished Lecture in Mathematics Series

The series was established by UCR in 2005 to honor the mathematical contributions of Richard E. Block, Distinguished Professor of Mathematics Emeritus at UCR. The intent of the series is for UCR to have a lecture in pure mathematics approximately every other year by a distinguished mathematician, in honor of Prof. Block's contributions to mathematical research. The series is one of two such series presented by the UCR Mathematics Department honoring the department's two faculty members who achieved the rank of what is now called Distinguished Professor (the other series honors Victor Shapiro).

The second lecture in the Block Distinguished Lecture series is being given on Oct. 19, 2010 by Eric M. Friedlander, who is President-Elect of the American Mathematical Society and Dean's Professor of Mathematics at the University of Southern California; his title is "Elementary modular representation theory". The first lecture in the series was given on Nov. 1, 2007 by Efim Zelmanov, who was a Fields Medal recipient and the Rita L. Atkinson Chair in Mathematics at the University of California San Diego; his lecture's title was "The Specht problem and the linearity of pro-p groups".

Richard E. Block came to UCR in 1968 as a full professor. Born in 1931, he received his Ph.D. from the University of Chicago in 1956. Before coming to UCR, he had held faculty positions at Indiana University, Yale, Caltech, and the University of Illinois. At UCR, he was honored as the Academic Senate Faculty Research Lecturer in 1986; was advanced to the rank of Professor Above Scale, now called Distinguished Professor, in 1987; served as Department Chair 1988-89; and formally retired in 1994 but remained active in the following years.

Much of Prof. Block's research was on Lie algebras, especially Lie algebras of prime characteristic, but it also included work on associative and other non-associative rings and algebras, coalgebras, Hopf algebras, and combinatorial designs. A number of his theorems are now widely described as classical results. These include his theorem (Annals of Math, 1969) on differentiably simple rings with its application giving a structure theorem for semisimple Lie algebras at prime characteristic and (as subsequently noted by V. Kac) for semisimple Lie superalgebras at characteristic 0; his proof (PNAS, 1984 and J. Algebra, 1988), in joint work with Robert L. Wilson, of the Kostikin-Shafarevitch conjecture that restricted simple Lie algebras are of classical or Cartan type, which culminated the efforts on this topic for a half century by some of the world's leading algebraists; his inequality (Math. Zeit., 1967) on the numbers of point and block orbits, now a standard topic in graduate texts and monographs on combinatorial designs, usually referred to as "Block's Lemma"; and his classification and construction (Advances in Math., 1981) of all (infinite dimensional, characteristic 0) irreducible representations of the first Weyl algebra and of the Lie algebra sl2. He also was the first to construct (Trans. AMS, 1966) what later became known as the Virasoro Algebra. Even his earliest published work (Trans. AMS, 1958 for prime characteristic, and Proc. AMS, 1958 for characteristic 0), on what came to be known as Algebras of Block, continues to be used and cited internationally.