BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:[TMS Symposium] Finite subgroups of SL(2\,CC) and SL(3\,CC) and th
 eir role in algebraic geometry  - Prof. Miles Reid FRS (Warwick)
DTSTART:20160221T163000Z
DTEND:20160221T173000Z
UID:TALK64759@talks.cam.ac.uk
CONTACT:Jason Kwong
DESCRIPTION:Felix Klein classified the finite subgroups of SL(2\,CC) aroun
 d 1860\; there are two infinite families\ncorresponding to regular polygon
 s in the plane\, together with three exceptional groups of order 24\, 48\n
 and 120 that are "spinor" double covers of the symmetry groups of the regu
 lar polyhedra (the\ntetrahedron\, octahedron and icosahedron). The finite 
 subgroups of SL(3\,CC) are also classified (and\nalso SL(n\,CC) for higher
  n)\, although the problem gets harder and it is not clear how to view the
 \nassortment of solutions with any pretence to elegance.\nThe quotient spa
 ces X = CC^2/G by Klein's finite subgroups G in SL(2\,CC) form a very\nrem
 arkable family of isolated surface singularities\, that were studied by Du
  Val during the 1930s\n(aided by Coxeter). Du Val's work was central to th
 e study of algebraic surfaces during the 1970s and\n1980s\, and played a f
 oundational role in the study of algebraic 3-folds from the 1980s onwards.
  In the\n1980s McKay observed that the representation theory of the group 
 G is reflected in the geometry of\nthe resolution of singularities of X. T
 his correspondence has been generalised to 3-dimensions\, with\nthe same p
 roviso concerning the nature of the problem and its solutions.\n
LOCATION:Winstanley Lecture Theatre\, Trinity College
END:VEVENT
END:VCALENDAR