BEGIN:VCALENDAR VERSION:2.0 PRODID:-//wp-events-plugin.com//7.2.3.1//EN TZID:Europe/Paris X-WR-TIMEZONE:Europe/Paris BEGIN:VEVENT UID:6287@i2m.univ-amu.fr DTSTART;TZID=Europe/Paris:20211026T110000 DTEND;TZID=Europe/Paris:20211026T120000 DTSTAMP:20241120T201355Z URL:https://www.i2m.univ-amu.fr/evenements/compactifcations-of-hermitian-y ang-mills-moduli-space-and-the-yang-mills-flow-on-projective-manifolds/ SUMMARY:Benjamin Sibley (Université Libre de Bruxelles): Compactifications of Hermitian-Yang-Mills moduli space and the Yang-Mills flow on projectiv e manifolds DESCRIPTION:Benjamin Sibley: Title: Compactifications of Hermitian-Yang-Mi lls moduli space and the Yang-Mills flow on projective manifolds\n\nAbstra ct: One of the cornerstones of gauge theory and complex geometry in the l ate 20th century was the so-called "Kobayashi-Hitchin correspondence"\, wh ich 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\, this gives an identification of (non-compact) moduli spaces. On the other\, one proo f of the correspondence goes through a natural parabolic (up to gauge) flo w called Yang-Mills flow. Namely\, Donaldson proved the convergence of thi s flow to an Hermitian-Yang-Mills connection in the case that the initial holomorphic structure is stable. Two questions that this leaves open are:\ n1. Do the moduli spaces admit compactifications\, and if so what sort of structure do they have? Are they for example complex spaces? Complex proje ctive? What is the relationship between the compactifications on each side ?\n2. What is the behaviour of the flow at infinity in the case when the i nitial holomorphic structure is unstable? I will touch on aspects of my pr evious work on these problems and explain how they connect up with each ot her. 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.\n\n\n\n\n\n\n\n\nParamètres connexion Zoom:\n\nSujet : Sémi naire de Géométrie Complexe\n\nLien:\n\nhttps://univ-amu-fr.zoom.us/j/97 323268497?pwd=K2VYdjd4cTdCanQ0REVFY2tLTDlIUT09\n\nID de réunion : 973 23 26 8497\n\nCode secret: voir annonce par mail\n\n \;\n\n ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2 021/09/BenSibley-e1632147898524.jpg CATEGORIES:Séminaire,Géométrie Complexe END:VEVENT BEGIN:VTIMEZONE TZID:Europe/Paris X-LIC-LOCATION:Europe/Paris BEGIN:DAYLIGHT DTSTART:20210328T030000 TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST END:DAYLIGHT END:VTIMEZONE END:VCALENDAR