BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Complete Complexes and Spectral Sequences - Evangelos Routis\, Uni
 versity of Warwick 
DTSTART:20191204T141500Z
DTEND:20191204T151500Z
UID:TALK132859@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:The space of complete collineations is an important and beauti
 ful chapter of algebraic geometry\, which has its origins in the classical
  works of Chasles\, Schubert and many others\, dating back to the 19th cen
 tury. It provides a 'wonderful compactification' (i.e. smooth with normal 
 crossings boundary) of the space of full-rank maps between two (fixed) vec
 tor spaces. More recently\, the space of complete collineations has been s
 tudied intensively and has been used to derive groundbreaking results in d
 iverse areas of mathematics. One such striking example is L. Lafforgue's c
 ompactification of the stack of Drinfeld's shtukas\, which he subsequently
  used to prove the Langlands correspondence for the general linear group. 
  \n\nIn joint work with M. Kapranov\, we look at these classical spaces fr
 om a modern perspective: a complete collineation is simply a spectral sequ
 ence of two-term complexes of vector spaces. We develop a theory involving
  more full-fledged (simply graded) spectral sequences with arbitrarily man
 y terms. We prove that the set of such spectral sequences has the structur
 e of a smooth projective variety\, the 'variety of complete complexes'\, w
 hich provides a desingularization\, with normal crossings boundary\, of th
 e 'Buchsbaum-Eisenbud variety of complexes'\, i.e. a 'wonderful compactifi
 cation' of the union of its maximal strata.
LOCATION:CMS MR3
END:VEVENT
END:VCALENDAR