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SUMMARY:Compactifcations of Hermitian-Yang-Mills moduli space and the Yang
 -Mills flow on projective manifolds - Ben Sibley\, Université Libre de Br
 uxelles
DTSTART:20191120T141500Z
DTEND:20191120T151500Z
UID:TALK129862@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:One of the cornerstones of gauge theory and complex geometry i
 n the late 20th century was the so-called "Kobayashi-Hitchin correspondenc
 e"\, which provides a link between Hermitian-Yang-Mills connections (gauge
  theory) and stable holomorphic structures (complex geometry) on a vector 
 bundle over projective (or merely Kähler) manifold. On the one hand\, thi
 s gives an identification of (non-compact) moduli spaces. On the other\, o
 ne proof of the correspondence goes through a natural parabolic (up to gau
 ge) flow called Yang-Mills flow. Namely\, Donaldson proved the convergence
  of this flow to an Hermitian-Yang-Mills connection in the case that the i
 nitial holomorphic structure is stable. Two questions that this leaves ope
 n are: 1. Do the moduli spaces admit compactifications\, and if so what so
 rt of structure do they have? Are they for example complex spaces? Complex
  projective? What is the relationship between the compactifications on eac
 h side? 2. What is the behaviour of the flow at infinity in the case when 
 the initial holomorphic structure is unstable? I will touch on aspects of 
 my previous work on these problems and explain how they connect up with ea
 ch other. This work is spread out over several papers\, and is partly join
 t work with Richard Wentworth\, and with Daniel Greb\, Matei Toma\, and Ri
 chard Wentworth.
LOCATION:CMS MR13
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