BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Compactifcations of Hermitian-Yang-Mills moduli sp
ace and the Yang-Mills flow on projective manifold
s - Ben Sibley\, Université Libre de Bruxelles
DTSTART;TZID=Europe/London:20191120T141500
DTEND;TZID=Europe/London:20191120T151500
UID:TALK129862AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/129862
DESCRIPTION:One of the cornerstones of gauge theory and comple
x geometry in the late 20th century was the so-cal
led "Kobayashi-Hitchin correspondence"\, which pro
vides a link between Hermitian-Yang-Mills connecti
ons (gauge theory) and stable holomorphic structur
es (complex geometry) on a vector bundle over proj
ective (or merely Kähler) manifold. On the one han
d\, this gives an identification of (non-compact)
moduli spaces. On the other\, one proof of the cor
respondence goes through a natural parabolic (up t
o gauge) flow called Yang-Mills flow. Namely\, Don
aldson proved the convergence of this flow to an H
ermitian-Yang-Mills connection in the case that th
e initial holomorphic structure is stable. Two que
stions that this leaves open are: 1. Do the moduli
spaces admit compactifications\, and if so what s
ort of structure do they have? Are they for exampl
e complex spaces? Complex projective? What is the
relationship between the compactifications on each
side? 2. What is the behaviour of the flow at inf
inity in the case when the initial holomorphic str
ucture is unstable? I will touch on aspects of my
previous work on these problems and explain how th
ey connect up with each other. This work is spread
out over several papers\, and is partly joint wor
k with Richard Wentworth\, and with Daniel Greb\,
Matei Toma\, and Richard Wentworth.
LOCATION:CMS MR13
CONTACT:Dhruv Ranganathan
END:VEVENT
END:VCALENDAR