BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Kyle Broder (The University of Queensland) DTSTART:20240327T230000Z DTEND:20240327T235900Z DTSTAMP:20260423T052922Z UID:VSGS/88 DESCRIPTION:Title: In variant metrics in complex analysis and a conjecture of Kobayashi and Lang \nby Kyle Broder (The University of Queensland) as part of Virtual sem inar on geometry with symmetries\n\n\nAbstract\nA compact complex manifold $X$ is declared Kobayashi hyperbolic if every holomorphic map from the co mplex plane into $X$ is constant. Kobayashi hyperbolic manifolds have main tained a central role in our understanding of the landscape of complex man ifolds since their introduction in 1967. One striking feature of complex g eometry is the capacity to encode this highly transcendental notion of hyp erbolicity in the coarse geometric language of distance functions that are invariant under the automorphism group and decrease under holomorphic map s. A long-standing conjecture of Kobayashi (1970) and Lang (1986) predicts that a compact Kobayashi hyperbolic Kähler manifold admits a Kähler—E instein metric of negative Ricci curvature. We will present the most gener al evidence for the Kobayashi—Lang conjecture: A compact Kähler manifol d with a pluriclosed metric of negative holomorphic curvature admits a uni que Kähler—Einstein metric of negative Ricci curvature. This result is a joint work with James Stanfield and comes from the first general improve ment on the Schwarz lemma for holomorphic maps between Hermitian manifolds since 1978.\n LOCATION:https://researchseminars.org/talk/VSGS/88/ END:VEVENT END:VCALENDAR