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Abstract: We plan to study Calabi-Yau threefolds with Picard number up to 2 or with complex moduli up to 2 dimensions. Conjecturally, CY3 in both classes are closely related under the global mirror map, which exchanges the A side (Kahler moduli) and the B side (complex moduli). Moreover, such a global mirror correspondence should also be compatible with extremal transitions. The mirror correspondence between quintic CY and its mirror quintic is the most well studied example. The famous BCOV theory on the B side suggests fundamental identities (e.g. Yamaguchi-Yau) on the A side and eventually helps to find methods to attack the higher genus curve counting for the quintics. Such a correspondence is mostly unknown for two parameter models except for the very recent preprint by Hosono and Takagi arXiv:2103.08150v2 on abelian fibered CY3. It is our hope that a closer study on the existing literature may lead to a better understanding on the subject. In doing so, we will discuss various topics on deformations of CY3, including the Bryant-Griffiths period map and toric GKZ systems with emphasizes on 1d or 2d models. Birational geometry on CY3 also form an essential technique and it appears that a good knowledge on non-Kahler CY3 is indispensable.

Topics and Speakers:

Higher genus counting of quintics
    You-Cheng CHOU (AS)
    Ping-Hsuan CHUANG (NTU)
    Po-Sheng WU (NTU)
Complex moduli, period maps and VHS
    Tsung-Ju LEE (CMSA Harvard, TIMS)
    Shuang-Yen LEE (NTU)
Birational geometry of CY3
    Sz-Sheng WANG (AS)
Constructions of non-Kahler CY3
    Hsueh-Yung LIN (NTU, NCTS)

BCOV theory
Chin-Lung WANG (NTU, TIMS)

Date: June 2, 6, 9, 13, 16, 2023
Time: 9:00 - 11:00, 13:00 - 15:00
Venue: Room 202, Astro-Math Building, NTU
Organizer: You-Cheng CHOU (Academi Sinica), Tsung-Ju LEE (CMSA Harvard, TIMS), Sz-Sheng WANG (Academia Sinica)

Available Talk List

2023-06-02 (Fri.)	Complex moduli, period maps and VHS I: Special Kahler geometry and BCOV theory Tsung-Ju Lee (CMSA Harvard, TIMS)
2023-06-02 (Fri.)	BCOV conjectures on quintic 3-folds You-Cheng Chou (Academia Sinica)
2023-06-06 (Tue.)	Constructions of non-Kähler K-trivial manifolds (after Clemens, Friedman, Reid, Hashimoto, Sano...) Hsueh-Yung Lin (NTU, NCTS)
2023-06-06 (Tue.)	LG/CY correspondence and the theory of Mixed-Spin-P fields Ping-Hsuan Chuang (NTU)
2023-06-09 (Fri.)	Cone structure of Calabi-Yau 3-folds of Picard number 2 Sz-Sheng Wang (Academia Sinica)
2023-06-09 (Fri.)	Complex moduli, period maps and VHS II: GKZ systems and the secondary fan moduli Shuang-Yen Lee (NTU)
2023-06-13 (Tue.)	Complex moduli, period maps and VHS III: Topological string amplitudes and the finite generation theorem Tsung-Ju Lee (CMSA Harvard, TIMS)
2023-06-13 (Tue.)	The NMSP theory and Yamaguchi-Yau's polynomial structure Po-Sheng Wu (NTU)
2023-06-16 (Fri.)	Examples of Calabi-Yau 3-folds with small parameters Sz-Sheng Wang (Academia Sinica)
2023-06-16 (Fri.)	BCOV for 2 parameters and boundary effects arising from GLSM Chin-Lung Wang (NTU, TIMS)