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DTSTART;TZID=America/New_York:20220302T093000
DTEND;TZID=America/New_York:20220302T223000
DTSTAMP:20240301T113401Z
CREATED:20240214T092842Z
LAST-MODIFIED:20240301T113401Z
UID:10002629-1646213400-1646260200@cmsa.fas.harvard.edu
SUMMARY:Tropical Lagrangian multi-sections and locally free sheaves
DESCRIPTION:Abstract: The SYZ proposal suggests that mirror symmetry is T-duality. It is a folklore that locally free sheaves are mirror to a Lagrangian multi-section of the SYZ fibration. In this talk\, I will introduce the notion of tropical Lagrangian multi-sections and discuss how to obtain from such object to a class of locally free sheaves on the log Calabi-Yau spaces that Gross-Siebert have considered. I will also discuss a joint work with Kwokwai Chan and Ziming Ma\, where we proved the smoothability of a class of locally free sheaves on some log Calabi-Yau surfaces by using combinatorial data obtained from tropical Lagrangian multi-sections.
URL:https://cmsa.fas.harvard.edu/event/3-1-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220302_Yat-Hin-SUEN_poster-1.png
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DTSTART;TZID=America/New_York:20220315T100000
DTEND;TZID=America/New_York:20220315T230000
DTSTAMP:20240301T113301Z
CREATED:20240214T092307Z
LAST-MODIFIED:20240301T113301Z
UID:10002622-1647338400-1647385200@cmsa.fas.harvard.edu
SUMMARY:Birkhoff’s conjecture on integrable billiards and Kac’s problem “hearing the shape of a drum”
DESCRIPTION:Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level\, the analogous conjecture is that ellipses are uniquely determined by their Dirichlet (or\, Neumann) eigenvalues. Using the results on the Birkhoff conjecture\, Hamid Hezari and I proved that for ellipses of small eccentricity are indeed uniquely determined by their eigenvalues. Except for disks\, which Kac proved to be uniquely determined\, these are the only domains for which it is known that one can hear their shape.
URL:https://cmsa.fas.harvard.edu/event/3-15-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220330T093000
DTEND;TZID=America/New_York:20220330T103000
DTSTAMP:20240301T113038Z
CREATED:20240214T080954Z
LAST-MODIFIED:20240301T113038Z
UID:10002582-1648632600-1648636200@cmsa.fas.harvard.edu
SUMMARY:Elliptic chiral homology and chiral index
DESCRIPTION:Abstract: We present an effective quantization theory for chiral deformation of two-dimensional conformal field theories. We explain a connection between the quantum master equation and the chiral homology for vertex operator algebras. As an application\, we construct correlation functions of the curved beta-gamma/b-c system and establish a coupled equation relating to chiral homology groups of chiral differential operators. This can be viewed as the vertex algebra analogue of the trace map in algebraic index theory. The talk is based on the recent work arXiv:2112.14572 [math.QA].
URL:https://cmsa.fas.harvard.edu/event/3-29-2022-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20220330_Si-LI_poster-1.png
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