BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schre ieder DTSTART:20200721T150000Z DTEND:20200721T160000Z DTSTAMP:20260422T212827Z UID:tacos/1 DESCRIPTION:Title: Co homology and Characteristic Classes of (almost) complex manifolds\nby Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schreieder as part of Geometry and TACoS\n\n\nAbstract\nThis is the live discussion for the session "Cohomology and Characteristic Classes of (Almost) Complex Ma nifolds"\, see https://researchseminars.org/talk/tacos/3/ \, including the following talks:\n\n- Joana Cirici (Universitat de Barcelona): “Dolbeau lt cohomology for almost complex manifolds”\n\n- Jean-Pierre Demailly (I nstitut Fourier\, Université Grenoble Alpes) “On the approximate cohomo logy of quasi holomorphic line bundles”\n\n- Claude LeBrun (Stony Brook) : "Einstein Metrics\, Weyl Curvature\, and Anti-Holomorphic Involutions"\n \n- Stefan Schreieder (Leibniz Universität Hannover): “Holomorphic one- forms without zeros on threefolds”\n LOCATION:https://researchseminars.org/talk/tacos/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schre ieder DTSTART:20200707T070000Z DTEND:20200707T080000Z DTSTAMP:20260422T212827Z UID:tacos/3 DESCRIPTION:Title: Co homology and Characteristic Classes of (almost) complex manifolds\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/ END:VEVENT BEGIN:VEVENT SUMMARY:Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske DTSTART:20200901T054500Z DTEND:20200901T064500Z DTSTAMP:20260422T212827Z UID:tacos/4 DESCRIPTION:Title: Ni lmanifold and Solvmanifold Techniques in Complex Geometry\nby Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske as part of Geome try and TACoS\n\n\nAbstract\n- Viviana del Barco (Université Paris-Saclay and UNR-CONICET): "Killing forms on nilpotent Lie groups"\n\nAbstract. Ki lling forms on Riemannian manifolds are differential forms whose covariant derivative with respect to the Levi-Civita connection is totally skew-sym metric. They generalize to higher degrees the concept of Killing vector fi elds.\nExamples of Riemannian manifolds with non-parallel Killing $k$-form s are quite rare for $k\\geq 2$. Nevertheless they appear\, for instance\, on nearly-K\\"ahler manifolds\, round spheres and Sasakian manifolds. The aim of this talk is to introduce recent results regarding the structure o f 2-step nilpotent Lie groups endowed with left-invariant Riemannian metr ic and carrying non-trivial Killing forms. In the way\, we will review asp ects of the Riemannian geometry of nilpotent Lie groups endowed with left- invariant metrics and describe the methods to achieve the structure result s. The talk is based on joint works with Andrei Moroianu (CNRS\, France).\ n\n\n- Anna Fino (Università di Torino): "SKT metrics on nilmanifolds and solvmanifolds"\n\nAbstact. An SKT (or pluriclosed) metric on a complex m anifold is an Hermitian metric whose fundamental form is $\\partial \\over line \\partial$-closed.\nI will present some general results about SKT met rics on compact nilmanifolds and solvmanifolds\,  considering also the li nk with symplectic geometry and generalized Kähler geometry.\n\n\n- Hisas hi Kasuya (Osaka University): "Results and problems on cohomology of solvm anifolds"\n\nAbstract. One of the reasons why nilmanifolds and solvmanif olds provide many interesting examples for various geometries is that we c an compute cohomology of them well. The contents of my video talk are as f ollows:\n(1) I will give an overview of the study of de Rham and Dolbeault cohomology of nilmanifolds and solvmanifolds.\n(2) I will explain detail s of techniques of computing cohomology of solvmanifolds I constructed. \n(3) I will suggest an unsolved problem on Dolbeault cohomology of solvm anifolds with some observations on Oeljeklaus-Toma manifolds.\n\n\n- Sön ke Rollenske (Philipps-Universität Marburg): "Dolbeault cohomology of com plex nilmanifolds"\n\nAbstract. By Nomizu's theorem\, the de Rham cohomol ogy of a compact nilmanifold $M=\\Gamma \\backslash G$ can be represented by left-invariant  differential forms\, that is\, it can be computed fro m the Lie-algebra and does not depend on the lattice $\\Gamma$.\nIf M is e ndowed with a left-invariant complex structure J\, it is  natural to ask the same property for Dolbeault cohomology. I will sketch what is known a nd why\, from a practical point of view\, all relevant cases are already c overed.\nStarting from a key example\, I will explain\, why more recent ap proaches studying foliations instead of fibrations were neccessary to sett le the case of real dimension six.\n\nThe discussion is open at https://gi tter.im/GTACOS-September2020/. The live discussion with the speakers for t his series of talks will be held on September 15\, see https://researchsem inars.org/talk/tacos/5/\n LOCATION:https://researchseminars.org/talk/tacos/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske DTSTART:20200915T130000Z DTEND:20200915T140000Z DTSTAMP:20260422T212827Z UID:tacos/5 DESCRIPTION:Title: Ni lmanifold and Solvmanifold Techniques in Complex Geometry\nby Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske as part of Geome try and TACoS\n\n\nAbstract\nThis is the live discussion for the session " Nilmanifold and Solvmanifold Techniques in Complex Geometry"\, see https:/ /researchseminars.org/talk/tacos/4/ \, including the following talks:\n\n- Viviana del Barco (Université Paris-Saclay and UNR-CONICET): "Killing fo rms on nilpotent Lie groups"\n\n- Anna Fino (Università di Torino): “SK T metrics on nilmanifolds and solvmanifolds”\n\n- Hisashi Kasuya (Osaka University): "Results and problems on cohomology of solvmanifolds"\n\n- S önke Rollenske (Philipps-Universität Marburg): “Dolbeault cohomology o f complex nilmanifolds”\n LOCATION:https://researchseminars.org/talk/tacos/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bakker\, Daniel Huybrechts\, Andrew Swann\, Claire Voisin DTSTART:20201103T064500Z DTEND:20201103T070000Z DTSTAMP:20260422T212827Z UID:tacos/6 DESCRIPTION:Title: Hy perkähler Geometry\nby Benjamin Bakker\, Daniel Huybrechts\, Andrew S wann\, Claire Voisin as part of Geometry and TACoS\n\n\nAbstract\n- Benjam in Bakker (University of Illinois at Chicago): "Towards a BBDGGHKP decompo sition theorem for nonprojective Calabi–Yau varieties"\n\nAbstract. Cala bi-Yau manifolds are built out of simple pieces by the Beauville–Bogomol ov decomposition theorem: any Calabi–Yau Kahler manifold up to an etale cover is a product of complex tori\, irreducible holomorphic symplectic ma nifolds\, and strict Calabi-Yau manifolds (which have no holomorphic forms except a holomorphic volume form). Work of Druel–Guenancia–Greb–Hor ing–Kebekus–Peternell over the last decade has culminated in a general ization of this result to projective Calabi–Yau varieties with the kinds of singularities that arise in the MMP\, and the proofs heavily use algeb raic methods. In this talk I will describe some work in progress with C. L ehn and H. Guenancia extending the decomposition theorem to nonprojective varieties via deformation theory. I will also discuss applications to the K-trivial case of a conjecture of Peternell asserting that any minimal Ka hler space can be approximated by algebraic varieties.\n\n- Daniel Huybrec hts (Universität Bonn): "3 families of K3 surfaces"\n\nAbstract. I will r eview three one-dimensional families of K3 surfaces (twistor\, Brauer or T ate-Shafarevich\, and Dwork) and explain how\, from a purely Hodge-theoret ic perspective\, they fit into one picture. I am particularly interested i n understanding how certain properties propagate along those families.\n\n - Andrew Swann (Aarhus University): "HyperKähler metrics and symmetries"\ n\nAbstract. HyperKähler metrics are surveyed and discussed from the poin t of view of Lie group symmetries\, so principally in the non-compact case . This includes the Gibbons-Hawking ansatz in dimension four\, cotangent b undles\, coadjoint orbits. A common theme is quotient constructions and va rious ideas related to symplectic reduction. Relations to other geometric structures naturally arise and show that metrics of indefinite signature h ave an important role.\n\n- Claire Voisin (Collège de France): "On the Le fschetz standard conjecture for hyper-Kähler manifolds"\n\nAbstract. The Lefschetz standard conjecture is of major importance in the theory of mot ives. It is open starting from degree 2 and in that degree\, it predicts t hat any holomorphic 2-form on a smooth projective manifold is induced from a 2-form on a surface by a correspondence. I will discuss some results an d further expectations in the hyper-Kähler setting.\n\nThe discussion is open at https://gitter.im/GTACOS-November2020/. The live discussion with t he speakers for this series of talks will be held on November 18\, see htt ps://researchseminars.org/talk/tacos/7/\n LOCATION:https://researchseminars.org/talk/tacos/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bakker\, Daniel Huybrechts\, Andrew Swann\, Claire Voisin DTSTART:20201118T160000Z DTEND:20201118T170000Z DTSTAMP:20260422T212827Z UID:tacos/7 DESCRIPTION:Title: Hy perkähler Geometry\nby Benjamin Bakker\, Daniel Huybrechts\, Andrew S wann\, Claire Voisin as part of Geometry and TACoS\n\n\nAbstract\nThis is the live discussion for the session "Hyperkähler Geometry"\, see https:// researchseminars.org/talk/tacos/6/ \, including the following talks:\n\n- Benjamin Bakker (University of Illinois at Chicago): "Towards a BBDGGHKP d ecomposition theorem for nonprojective Calabi–Yau varieties"\n\n- Daniel Huybrechts (Universität Bonn): "3 families of K3 surfaces"\n\n- Andrew S wann (Aarhus University): "HyperKähler metrics and symmetries"\n\n- Clair e Voisin (Collège de France): "On the Lefschetz standard conjecture for hyper-Kähler manifolds"\n LOCATION:https://researchseminars.org/talk/tacos/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Tang Fei\, Xenia de la Ossa\, Roberto Rubio\, Valentino Tosatti DTSTART:20210127T064500Z DTEND:20210127T070000Z DTSTAMP:20260422T212827Z UID:tacos/8 DESCRIPTION:Title: Ge ometry and Physics of Non-Kahler Calabi-Yau\nby Tang Fei\, Xenia de la Ossa\, Roberto Rubio\, Valentino Tosatti as part of Geometry and TACoS\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/tacos/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Tang Fei\, Xenia de la Ossa\, Roberto Rubio\, Valentino Tosatti DTSTART:20210210T160000Z DTEND:20210210T170000Z DTSTAMP:20260422T212827Z UID:tacos/9 DESCRIPTION:Title: Ge ometry and Physics of Non-Kahler Calabi-Yau\nby Tang Fei\, Xenia de la Ossa\, Roberto Rubio\, Valentino Tosatti as part of Geometry and TACoS\n\ nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/tacos/9/ END:VEVENT END:VCALENDAR