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:20260404T094701Z UID:tacos/1 DESCRIPTION:Title: Cohomology and Characteristic Classes of (almost) complex manifolds\nby Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schrei eder as part of Geometry and TACoS\n\n\nAbstract\nThis is the live discuss ion for the session "Cohomology and Characteristic Classes of (Almost) Com plex Manifolds"\, see https://researchseminars.org/talk/tacos/3/ \, includ ing the following talks:\n\n- Joana Cirici (Universitat de Barcelona): “ Dolbeault cohomology for almost complex manifolds”\n\n- Jean-Pierre Dema illy (Institut Fourier\, Université Grenoble Alpes) “On the approximate cohomology of quasi holomorphic line bundles”\n\n- Claude LeBrun (Stony Brook): "Einstein Metrics\, Weyl Curvature\, and Anti-Holomorphic Involut ions"\n\n- Stefan Schreieder (Leibniz Universität Hannover): “Holomorph ic one-forms without zeros on threefolds”\n LOCATION:https://stable.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:20260404T094701Z UID:tacos/3 DESCRIPTION:Title: Cohomology and Characteristic Classes of (almost) complex manifolds\nby Joana Cirici\, Jean-Pierre Demailly\, Claude LeBrun\, Stefan Schrei eder as part of Geometry and TACoS\n\n\nAbstract\n- Joana Cirici (Universi tat de Barcelona): “Dolbeault cohomology for almost complex manifolds” \n\nAbstract. I will introduce a Frölicher-type spectral sequence that is valid for all almost complex manifolds\, yielding a natural Dolbeault coh omology theory for non-integrable structures. I will revise the harmonic t heory surrounding Dolbeault cohomology and explain some applications to ni lmanifolds and nearly Kähler manifolds. This is joint work with Scott Wil son.\n\n- Jean-Pierre Demailly (Institut Fourier\, Université Grenoble Al pes) “On the approximate cohomology of quasi holomorphic line bundles” \n\nAbstract. Given a non rational Bott-Chern cohomology class of type (1\ ,1) on a complex manifolds\, there exists a sequence of “quasi holomorph ic” line bundles whose Chern classes approximate very closely certain mu ltiples of the given cohomology class. We will report on spectral estimate s provided by L. Laeng in his PhD thesis (2002)\, in relation with a numbe r of newer ideas emerging e.g. from our recent study of Bergman vector bun dles. We hope that these techniques could possibly be helpful to approach the conjectures on transcendental holomorphic Morse inequalities and Kähl er invariance of plurigenera.\n\n- Claude LeBrun (Stony Brook): "Einstein Metrics\, Weyl Curvature\, and Anti-Holomorphic Involutions"\n\nAbstract. A Riemannian metric is said to be Einstein if it has constant Ricci curvat ure. Dimension four is in many respects a privileged realm for Einstein m etrics. In particular\, there are certain 4-manifolds\, such as K3 and com plex ball-quotients\, where every Einstein metric comes from Kaehler geome try\, and where the moduli space of Einstein metrics can therefore be sho wn to be connected. In this lecture\, I will discuss analogous but weaker results that characterize the known Einstein metrics on the ten smooth co mpact 4-manifolds that arise as del Pezzo surfaces\, as well as on a famil y of five closely-related 4-manifolds that do not even admit almost-comple x structures.\n\n- Stefan Schreieder (Leibniz University Hannover): “Hol omorphic one-forms without zeros on threefolds”\n\nAbstract. We show tha t a smooth complex projective threefold admits a holomorphic one-form with out zeros if and only if the underlying real 6-manifold is a smooth fibre bundle over the circle\, and we give a complete classification of all thre efolds with that property. Our results prove a conjecture of Kotschick in dimension three. Joint work with Feng Hao.\n\nThe discussion is open at ht tps://gitter.im/GTACOS-July2020/.\nThe live discussion with the speakers f or this series of talks will be held on July 21\, see https://researchsemi nars.org/talk/tacos/1/\n LOCATION:https://stable.researchseminars.org/talk/tacos/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske DTSTART:20200901T054500Z DTEND:20200901T064500Z DTSTAMP:20260404T094701Z UID:tacos/4 DESCRIPTION:Title: Nilmanifold and Solvmanifold Techniques in Complex Geometry\nby V iviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske as part o f Geometry and TACoS\n\n\nAbstract\n- Viviana del Barco (Université Paris -Saclay and UNR-CONICET): "Killing forms on nilpotent Lie groups"\n\nAbstr act. Killing forms on Riemannian manifolds are differential forms whose co variant derivative with respect to the Levi-Civita connection is totally s kew-symmetric. They generalize to higher degrees the concept of Killing ve ctor fields.\nExamples of Riemannian manifolds with non-parallel Killing $ k$-forms are quite rare for $k\\geq 2$. Nevertheless they appear\, for ins tance\, on nearly-K\\"ahler manifolds\, round spheres and Sasakian manifol ds. The aim of this talk is to introduce recent results regarding the stru cture of 2-step nilpotent Lie groups endowed with left-invariant Riemanni an metric and carrying non-trivial Killing forms. In the way\, we will rev iew aspects of the Riemannian geometry of nilpotent Lie groups endowed wit h left-invariant metrics and describe the methods to achieve the structure results. The talk is based on joint works with Andrei Moroianu (CNRS\, Fr ance).\n\n\n- Anna Fino (Università di Torino): "SKT metrics on nilmanifo lds and solvmanifolds"\n\nAbstact. An SKT (or pluriclosed) metric on a co mplex manifold is an Hermitian metric whose fundamental form is $\\partial \\overline \\partial$-closed.\nI will present some general results about SKT metrics on compact nilmanifolds and solvmanifolds\,  considering also the link with symplectic geometry and generalized Kähler geometry.\n\n\n - Hisashi Kasuya (Osaka University): "Results and problems on cohomology o f solvmanifolds"\n\nAbstract. One of the reasons why nilmanifolds and so lvmanifolds provide many interesting examples for various geometries is th at we can compute cohomology of them well. The contents of my video talk a re as follows:\n(1) I will give an overview of the study of de Rham and Do lbeault cohomology of nilmanifolds and solvmanifolds.\n(2) I will explain details of techniques of computing cohomology of solvmanifolds I const ructed.\n(3) I will suggest an unsolved problem on Dolbeault cohomology o f solvmanifolds with some observations on Oeljeklaus-Toma manifolds.\n\n\ n- Sönke Rollenske (Philipps-Universität Marburg): "Dolbeault cohomology of complex nilmanifolds"\n\nAbstract. By Nomizu's theorem\, the de Rham cohomology of a compact nilmanifold $M=\\Gamma \\backslash G$ can be repr esented by left-invariant  differential forms\, that is\, it can be compu ted from the Lie-algebra and does not depend on the lattice $\\Gamma$.\nIf M is endowed with a left-invariant complex structure J\, it is  natural to ask the same property for Dolbeault cohomology. I will sketch what is known and why\, from a practical point of view\, all relevant cases are al ready covered.\nStarting from a key example\, I will explain\, why more re cent approaches studying foliations instead of fibrations were neccessary to settle the case of real dimension six.\n\nThe discussion is open at htt ps://gitter.im/GTACOS-September2020/. The live discussion with the speaker s for this series of talks will be held on September 15\, see https://rese archseminars.org/talk/tacos/5/\n LOCATION:https://stable.researchseminars.org/talk/tacos/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Viviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske DTSTART:20200915T130000Z DTEND:20200915T140000Z DTSTAMP:20260404T094701Z UID:tacos/5 DESCRIPTION:Title: Nilmanifold and Solvmanifold Techniques in Complex Geometry\nby V iviana del Barco\, Anna Fino\, Hisashi Kasuya\, Sönke Rollenske as part o f Geometry and TACoS\n\n\nAbstract\nThis is the live discussion for the se ssion "Nilmanifold and Solvmanifold Techniques in Complex Geometry"\, see https://researchseminars.org/talk/tacos/4/ \, including the following talk s:\n\n- Viviana del Barco (Université Paris-Saclay and UNR-CONICET): "Kil ling forms on nilpotent Lie groups"\n\n- Anna Fino (Università di Torino) : “SKT metrics on nilmanifolds and solvmanifolds”\n\n- Hisashi Kasuya (Osaka University): "Results and problems on cohomology of solvmanifolds"\ n\n- Sönke Rollenske (Philipps-Universität Marburg): “Dolbeault cohomo logy of complex nilmanifolds”\n LOCATION:https://stable.researchseminars.org/talk/tacos/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bakker\, Daniel Huybrechts\, Andrew Swann\, Claire Voisin DTSTART:20201103T064500Z DTEND:20201103T070000Z DTSTAMP:20260404T094701Z UID:tacos/6 DESCRIPTION:Title: Hyperkähler Geometry\nby Benjamin Bakker\, Daniel Huybrechts\, A ndrew Swann\, Claire Voisin as part of Geometry and TACoS\n\n\nAbstract\n- Benjamin Bakker (University of Illinois at Chicago): "Towards a BBDGGHKP decomposition theorem for nonprojective Calabi–Yau varieties"\n\nAbstrac t. Calabi-Yau manifolds are built out of simple pieces by the Beauville– Bogomolov decomposition theorem: any Calabi–Yau Kahler manifold up to an etale cover is a product of complex tori\, irreducible holomorphic symple ctic manifolds\, and strict Calabi-Yau manifolds (which have no holomorphi c forms except a holomorphic volume form). Work of Druel–Guenancia–Gre b–Horing–Kebekus–Peternell over the last decade has culminated in a generalization of this result to projective Calabi–Yau varieties with th e kinds of singularities that arise in the MMP\, and the proofs heavily us e algebraic methods. In this talk I will describe some work in progress wi th C. Lehn and H. Guenancia extending the decomposition theorem to nonproj ective varieties via deformation theory. I will also discuss applications to the K-trivial case of a conjecture of Peternell asserting that any min imal Kahler space can be approximated by algebraic varieties.\n\n- Daniel Huybrechts (Universität Bonn): "3 families of K3 surfaces"\n\nAbstract. I will review three one-dimensional families of K3 surfaces (twistor\, Brau er or Tate-Shafarevich\, and Dwork) and explain how\, from a purely Hodge- theoretic perspective\, they fit into one picture. I am particularly inter ested in understanding how certain properties propagate along those famili es.\n\n- Andrew Swann (Aarhus University): "HyperKähler metrics and symme tries"\n\nAbstract. HyperKähler metrics are surveyed and discussed from t he point of view of Lie group symmetries\, so principally in the non-compa ct case. This includes the Gibbons-Hawking ansatz in dimension four\, cota ngent bundles\, coadjoint orbits. A common theme is quotient constructions and various ideas related to symplectic reduction. Relations to other geo metric structures naturally arise and show that metrics of indefinite sign ature have an important role.\n\n- Claire Voisin (Collège de France): "On the Lefschetz standard conjecture for hyper-Kähler manifolds"\n\nAbstra ct. The Lefschetz standard conjecture is of major importance in the theory of motives. It is open starting from degree 2 and in that degree\, it pre dicts that any holomorphic 2-form on a smooth projective manifold is induc ed from a 2-form on a surface by a correspondence. I will discuss some res ults and further expectations in the hyper-Kähler setting.\n\nThe discuss ion is open at https://gitter.im/GTACOS-November2020/. The live discussion with the speakers for this series of talks will be held on November 18\, see https://researchseminars.org/talk/tacos/7/\n LOCATION:https://stable.researchseminars.org/talk/tacos/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Bakker\, Daniel Huybrechts\, Andrew Swann\, Claire Voisin DTSTART:20201118T160000Z DTEND:20201118T170000Z DTSTAMP:20260404T094701Z UID:tacos/7 DESCRIPTION:Title: Hyperkähler Geometry\nby Benjamin Bakker\, Daniel Huybrechts\, A ndrew Swann\, Claire Voisin as part of Geometry and TACoS\n\n\nAbstract\nT his is the live discussion for the session "Hyperkähler Geometry"\, see h ttps://researchseminars.org/talk/tacos/6/ \, including the following talks :\n\n- Benjamin Bakker (University of Illinois at Chicago): "Towards a BBD GGHKP decomposition theorem for nonprojective Calabi–Yau varieties"\n\n- Daniel Huybrechts (Universität Bonn): "3 families of K3 surfaces"\n\n- A ndrew Swann (Aarhus University): "HyperKähler metrics and symmetries"\n\n - Claire Voisin (Collège de France): "On the Lefschetz standard conjectur e for hyper-Kähler manifolds"\n LOCATION:https://stable.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:20260404T094701Z UID:tacos/8 DESCRIPTION:Title: Geometry and Physics of Non-Kahler Calabi-Yau\nby Tang Fei\, Xeni a de la Ossa\, Roberto Rubio\, Valentino Tosatti as part of Geometry and T ACoS\n\nAbstract: TBA\n LOCATION:https://stable.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:20260404T094701Z UID:tacos/9 DESCRIPTION:Title: Geometry and Physics of Non-Kahler Calabi-Yau\nby Tang Fei\, Xeni a de la Ossa\, Roberto Rubio\, Valentino Tosatti as part of Geometry and T ACoS\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/tacos/9/ END:VEVENT END:VCALENDAR