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SUMMARY:Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schre
 ieder
DTSTART:20200707T070000Z
DTEND:20200707T080000Z
DTSTAMP:20260423T022839Z
UID:tacos/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/tacos/3/">Co
 homology and Characteristic Classes of (almost) complex manifolds</a>\nby 
 Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schreieder as
  part of Geometry and TACoS\n\n\nAbstract\n- Joana Cirici (Universitat de 
 Barcelona): “Dolbeault cohomology for almost complex manifolds”\n\nAbs
 tract. I will introduce a Frölicher-type spectral sequence that is valid 
 for all almost complex manifolds\, yielding a natural Dolbeault cohomology
  theory for non-integrable structures. I will revise the harmonic theory s
 urrounding Dolbeault cohomology and explain some applications to nilmanifo
 lds and nearly Kähler manifolds. This is joint work with Scott Wilson.\n\
 n- Jean-Pierre Demailly (Institut Fourier\, Université Grenoble Alpes) 
 “On the approximate cohomology of quasi holomorphic line bundles”\n\nA
 bstract. Given a non rational Bott-Chern cohomology class of type (1\,1) o
 n a complex manifolds\, there exists a sequence of “quasi holomorphic”
  line bundles whose Chern classes approximate very closely certain multipl
 es of the given cohomology class. We will report on spectral estimates pro
 vided by L. Laeng in his PhD thesis (2002)\, in relation with a number of 
 newer ideas emerging e.g. from our recent study of Bergman vector bundles.
  We hope that these techniques could possibly be helpful to approach the c
 onjectures on transcendental holomorphic Morse inequalities and Kähler in
 variance of plurigenera.\n\n- Claude LeBrun (Stony Brook): "Einstein Metri
 cs\, Weyl Curvature\, and Anti-Holomorphic Involutions"\n\nAbstract. A Rie
 mannian metric is said to be Einstein if it has constant Ricci curvature. 
 Dimension four is in many respects a privileged realm  for Einstein metric
 s. In particular\, there are certain 4-manifolds\, such as K3 and complex 
 ball-quotients\, where every Einstein metric comes from Kaehler geometry\,
  and where the moduli space of Einstein metrics can  therefore be shown to
  be  connected. In this lecture\, I will discuss analogous but weaker resu
 lts that characterize the known Einstein metrics on the ten smooth compact
  4-manifolds that arise as del Pezzo surfaces\, as well as on a family of 
 five closely-related 4-manifolds that do not even admit almost-complex str
 uctures.\n\n- Stefan Schreieder (Leibniz University Hannover): “Holomorp
 hic one-forms without zeros on threefolds”\n\nAbstract. We show that a s
 mooth complex projective threefold admits a holomorphic one-form without z
 eros if and only if the underlying real 6-manifold is a smooth fibre bundl
 e over the circle\, and we give a complete classification of all threefold
 s with that property. Our results prove a conjecture of Kotschick in dimen
 sion three. Joint work with Feng Hao.\n\nThe discussion is open at https:/
 /gitter.im/GTACOS-July2020/.\nThe live discussion with the speakers for th
 is series of talks will be held on July 21\, see https://researchseminars.
 org/talk/tacos/1/\n
LOCATION:https://researchseminars.org/talk/tacos/3/
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