Geometry and Representation Theory: A Conference in Honor of George Lusztig

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The grant provides funding for a conference highlighting recent developments and open problems in the field of geometric representation theory. The conference is to be held May 30 through June 3, 2006, at the Massachusetts Institute of Technology in Cambridge, Massachusetts. The conference will bring together leading scholars in the field to describe their latest research and to honor George Lusztig, who introduced (and is still introducing) many of the ideas that underlie geometric representation theory. Among the topics expected to be covered are quiver varieties and their role in representation theory; representations of groups over local fields and fields of positive characteristics; quantum groups; and character sheaves.Representation theory can be thought of as a natural extension of linear algebra. A representation of an algebraic object is a collection of matrices (possibly infinite dimensional) which encode properties of the algebraic object. Geometric representation theory refers to the program of using techniques from geometry to construct representations. The advantage of these constructions is that it is often easy to prove a property of the representation that would not be apparent otherwise; for example, that the representation has a nice basis or that certain matrix elements turn out to be positive integers. George Lusztig is a leading researcher in geometric representation theory, and the conference being supported will bring together many of the most distinguished scholars in the field to honor him. The grant will help to support graduate students and recent doctorates in order that they may attend this exciting conference.