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UID:3a12637191b6a339831c6872e092b4fc
CATEGORIES:Gauge Theory Learning Seminar
CREATED:20260401T141120
SUMMARY:Constructing aZ-stable bundles over projective surfaces
LOCATION:Hill 705 and Zoom
DESCRIPTION:Abstract: Motivated by the Donaldson–Uhlenbeck–Yau theorem, a common strate
 gy for studying gauge-theoretic equations is to relate them to a suitable n
 otion of stability. For any choice of polynomial central charge Z over a cl
 osed Kähler manifold X, one can define a Z-critical equation for connection
 s on a holomorphic vector bundle E→X. In the large volume regime, the exist
 ence of solutions to this equation is equivalent to the asymptotic Z-stabil
 ity (aZ-stability) of E.\n\nWhile all (Mumford) stable bundles are necessar
 ily aZ-stable, this talk explores the construction of bundles that are aZ-s
 table but not Mumford stable. I will present a construction of such bundles
  over projective surfaces in the specific case where the Z-critical equatio
 n corresponds to the deformed Hermitian–Yang–Mills (dHYM) equation.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong data-olk-copy-source="MessageBody">Abstract:</strong>&nbsp;Motiv
 ated by the Donaldson–Uhlenbeck–Yau theorem, a common strategy for studying
  gauge-theoretic equations is to relate them to a suitable notion of stabil
 ity. For any choice of polynomial central charge Z over a closed Kähler man
 ifold X, one can define a Z-critical equation for connections on a holomorp
 hic vector bundle E→X. In the large volume regime, the existence of solutio
 ns to this equation is equivalent to the asymptotic Z-stability (aZ-stabili
 ty) of E.<br><br>While all (Mumford) stable bundles are necessarily aZ-stab
 le, this talk explores the construction of bundles that are aZ-stable but n
 ot Mumford stable. I will present a construction of such bundles over proje
 ctive surfaces in the specific case where the Z-critical equation correspon
 ds to the deformed Hermitian–Yang–Mills (dHYM) equation.</p>
CONTACT:Luiz Lara (Université de Bretagne Occidentale)
DTSTAMP:20260826T211415
DTSTART;TZID=America/New_York:20260407T110000
DTEND;TZID=America/New_York:20260407T120000
SEQUENCE:0
TRANSP:OPAQUE
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