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Almost Complex Geometry Seminar
Department of Mathematics
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Spring 2021:Join Zoom MeetingMeeting ID: 825 6324 2686 Passcode: 999054 | |||||||
2/5: Prof. Teng Fei (Rutgers-Newark)
Abstract: The equations of flux compactifications of Type IIA superstrings were written down by Tomasiello and Tseng-Yau. To study these equations, we introduce a natural geometric flow on symplectic Calabi-Yau 6-manifolds. We prove the well-posedness of this flow and
establish the basic estimates. As an application, we make use of our flow to find optimal almost complex structures on certain homogeneous symplectic half-flat manifolds. This is based on joint work with Phong, Picard and Zhang.
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2/12: no meeting (University closed)
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2/19: Prof. Carlo Scarpa (SISSA)
Abstract: The Hitchin-cscK system (HcscK, for short) is a pair of PDEs for a Kahler metric and an infinitesimal deformation of the complex structure, that couple the constant scalar curvature equation with a weak holomorphicity condition on the infinitesimal deformation. The system is derived from a hyperkahler extension of the Fujiki-Donaldson interpretation of the scalar curvature as a moment map. In this talk I will review some aspects of this construction, to highlight the similarity with Hitchin's description of the Higgs bundles equations, and I will present some recent results, contained in arxiv:2006.06250, about solutions of the Hitchin-cscK system on toric and abelian varieties. This is joint work with Jacopo Stoppa.
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2/26: Prof. Francesco Pediconi (U. Florence)
Abstract: In this talk, we will consider Hermitian manifolds acted by a (real) compact Lie group by holomorphic isometries with principal orbit of codimension one. In particular, we will focus on a special class of these manifolds constructed by following Berard-Berger. On such spaces, we characterize the special Hermitian non-Kahler metrics, such as balanced, pluriclosed, locally conformally Kahler, and we provide new examples of inhomogeneous non-Kahler second-Chern-Einstein metrics. This is a joint work with Daniele Angella.
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3/5: Prof. Jonas Stelzig (LMU Munchen)
Abstract: In the first part of the talk, I will define promising looking candidates for Bott-Chern and Aeppli cohomology for almost complex manifolds which give rise to a ddbar-type condition that implies formality.
In the second part, I will report on work in progress with Giovanni Placini
and Rui Coelho, revolving around maximally non-integrable almost complex
structures, mostly limiting myself to real dimension 4, where we show an
h-principle, giving rise to many examples. A study of the Dolbeault and Bott Chern cohomologies
of such structures will lead to a more critical view on the notions
introduced in the first half of the talk.
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3/12: Prof. Alexandra Otiman (Roma Tre University)
Abstract:
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3/19: Xi Sisi Shen (Northwestern)
Abstract:
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4/2: no meeting (spring break)
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4/9: Prof. Nicoletta Tardini (University di Parma)
Abstract:
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