Jon Alperin University of Chicago Date and time: Mon, 04/15/2002 - 4:00pm Physics, Room 202 Cantrell Lectures Lecture 1 "Group representations, their applications and arithmetic" Monday, April 15, 2002 4:00 p.m. - 5:00 p.m. Physics Building, Room 202 (Refreshments will be served before the talk, at 3:30 p.m.) Representations of symmetric groups are a basic tool in physics and chemistry. But, in addition, representations of finite groups come up in many other places in science and examples will be given, leading to the "arithmetic" of representations and to research of current great importance in this direction. (This lecture will be accessible to a general audience of students and faculty interested in mathematics and science.) Lecture 2 "The general linear group" Tuesday, April 16, 2002 4:00 p.m. - 5:00 p.m. Boyd Graduate Studies Building, Room 328 (Refreshments will be served before the talk, at 3:30 p.m.) The most important group in mathematics is the general linear group GL(n,F) of non-singular matrices over a field F. Not the usual examples one sees in all undergraduate courses! The theory of these groups, plus an explanation as to their importance plus outstanding open problems will be discussed. (This lecture will be accessible to undergraduate mathematics and mathematics education majors.) Lecture 3 "Rings that are nearly the same" Wednesday, April 17, 2002 4:00 p.m. - 5:00 p.m. Boyd Graduate Studies Building, Room 328 (Refreshments will be served before the talk, at 3:30 p.m.) Rings that are closely related are a prominent topic in group representations. Even isomorphism is useful in unexpected ways, but more general notions, like Morita equivalence, stable equivalence and Rickard equivalence (derived equivalence for rings) all play important roles in related ways. Important outstanding conjectures involve these ideas.