9/15: CUNY is closed this day
9/22: Prof. Teng Fei (Rutgers)
Title: Recent Progress on Type IIA Flow
Abstract: Motivated by Type IIA superstring theory, the Type IIA flow is a weakly parabolic PDE of 3-forms defined on 6-dimensional symplectic Calabi-Yau manifolds. In this talk, we explore various geometric and analytic aspects of the Type IIA flow. In particular, we show that the Type IIA flow is dynamically stable, and we apply this result to prove the stability of Kahler Calabi-Yau manifolds under symplectic deformations. This is based on joint work with Phong, Picard, and Zhang.
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9/29: Prof. Scott Wilson (CUNY)
Title: A higher-homotopical BV-structure on the differential
forms of (almost) complex manifolds with compatible metric.
Abstract: In 1985 Koszul showed that the differential forms of a symplectic manifold has an additional second order operator; part of what is now called a differential BV-algebra. Subsequent work by Getzler, Barannivok-Kontseivich, and Manin describe this structure as a (genus zero) cohomological field theory on the de Rham cohomology, i.e. an action of the compactified moduli space of (genus zero) Riemann surfaces with marked points. Such structures, also known as (formal) Frobenius manifolds, or hypercommutative algebras, have numerous connections with the A-model and mirror symmetry.
In this talk I'll explain a natural generalization of this to (almost) complex
manifolds with compatible metrics, using a higher-homotopical notion of
BV-algebras. This relies on generalizations of the Kahler identities to the
complex-Hermitian case (due to Demailly) and to the almost-complex Hermitian
case (recently obtained by Fernandez and Hosmer). My goal is to explain the
setup, establish the existence of the higher-homotopy BV-structure, and give
some explicit examples of complex manifolds where these higher operations are
non-zero.
This constitutes work in progress with Joana Cirici.
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10/6: Shuang Liang (Columbia U.)
Title:
Continuity equation on Hermitian manifolds and its application
Abstract: I will discuss the continuity equation on Hermitian manifolds, introduced by La Nave-Tian and extended to Hermitian metrics by Sherman-Weinkove. We use the Calabi estimates to show that on a compact complex manifold, the Chern scalar curvature of a solution must blow up at a finite-time singularity. Additionally, starting from certain classes of initial data on Oeljeklaus-Toma manifolds, we prove Gromov-Hausdorff and smooth convergence of the metric to a particular non-negative (1,1)-form. This is joint work with Xi Sisi Shen and Kevin Smith.
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10/13:
Prof. Richard Hind (U. Notre Dame)
Title:
TBA
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10/20: Prof. Mahmoud Zeinalian (Lehman, CUNY)
Title: TBA
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10/27: Nikita Klemyatin (Columbia U.)
Title: TBA
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11/3: Prof. Kevin Sackel (UMass Amherst)
Title: TBA
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11/10: Prof. Anna Fino (Florida Int. U.)
Title: TBA
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11/17: Prof. David Pham (QCC, CUNY)
Title: TBA
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11/24:
no meeting (Thanksgiving)
Title:
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12/1:
TBA
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12/8:
TBA
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