Mathematics Colloquium
3:00 p.m.
Math Annex 1100
Alastair Craw
University of Utah
The McKay correspondence
By associating a graph to certain finite subgroups of SL(2,C),
John McKay uncovered a beautiful link between representations
of any such group and geometrical properties of a complex
surface determined uniquely by the group. Years later, several
string theorists conjectured that a similar statement should
hold for finite subgroups of SL(3,C). However, the suggestion
that a complex manifold of dimension three was uniquely
determined by a finite subgroup of SL(3,C) flatly contradicted
the ideology that had arisen throughout the 1980's that led
to Mori's Fields Medal in 1990. Nevertheless, the string
theorists were right!
I plan to review McKay's original observation before describing
why the physicists' conjecture was a surprise to the
algebrogeometric community. The main goal of the talk is
to explain why the physicists were indeed correct and to
mention very recent joint work with Akira Ishii which sheds
more light on this question from the algebrogeometric
point of view.
Refreshments will be served at 2:45 p.m. in the Faculty Lounge,
Math Annex (Room 1115).
