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京东 11.11 红包
Amanda Hirschi:Gromov-Witten Moduli Spaces的Global Kuranishi Charts和一个乘积公式
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https://www.youtube.com/watch?v=gM1vQJaHJGs 美国普林斯顿高等研究院 Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Seminar site:http://www.math.tau.ac.il/~sarabt/zoominar/ Three 20-min Research Talks Topic: Global Kuranishi Charts for Gromov-Witten Moduli Spaces and a Product Formula Speaker: Amanda Hirschi Affiliation: University of Cambridge Date: April 21, 2023 I will describe the construction of a global Kuranishi chart for moduli spaces of stable pseudoholomorphic maps of any genus and explain how this allows for a straightforward definition of GW invariants. For those not convinced of its usefulness, I will sketch how this can be used to obtain a formula for the GW invariants of a product. This is joint work with Mohan Swaminathan. 在数学中,尤其是在拓扑学中,Kuranishi structure是scheme structure的smooth analogue。 如果一个拓扑空间被赋予 Kuranishi structure,那么它在局部可以等同于光滑映射的零集,或者这样的零集被有限群的商。 Kuranishi structure是由日本数学家Kenji Fukaya和Kaoru Ono在研究辛几何中的Gromov-Witten不变量和Floer同调时引入的,并以日本数学家Masatake Kuranishi命名。 "Kuranishi spaces" are a class of geometric spaces introduced in 1990 by Fukaya and Ono, as the geometric structure on moduli spaces of J-holomorphic curves in a symplectic manifold, and used in the work of Fukaya, Oh, Ohta and Ono on Lagrangian Floer cohomology and Fukaya categories. Roughly, a Kuranishi space is a topological space X covered by an atlas of 'Kuranishi neighbourhoods' (V, E, Γ,s, ψ), each arising from Kodaira-Spencer-Kuranishi deformations theory. Fukaya–Ono's main goal was to define virtual cycles/chains for these, to be able to define Gromov–Witten invariants, Lagrangian Floer theory, etc. Kenji Fukaya , Yong-Geun Oh , Hiroshi Ohta , Kaoru Ono——《Kuranishi Structures and Virtual Fundamental Chains》:https://doi.org/10.1007/978-981-15-5562-6 Dusa McDuff——《Notes on Kuranishi Atlases》:https://doi.org/10.48550/arXiv.1411.4306 Dusa McDuff, Katrin Wehrheim——《The topology of Kuranishi atlases》:https://doi.org/10.48550/arXiv.1508.01844
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