Supercongruences for rigid hypergeometric Calabi--Yau threefold-数学学院
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Supercongruences for rigid hypergeometric Calabi--Yau threefold

发布时间:2018年06月11日 15:23   浏览次数:
报告人 Ling Long 年月 2018-06

报告题目:Supercongruences for rigid hypergeometric Calabi--Yau threefold

报告人:Ling Long

报告人单位:Louisiana State University





We establish the supercongruences for the fourteen rigid hypergeometric Calabi--Yau threefolds over $\mathbb Q$ conjectured by Rodriguez-Villegas in 2003. Two different approaches are implemented, and they both successfully apply to all the fourteen supercongruences. Our first method is based on Dwork's theory of $p$-adic unit roots, and it allows us to establish the supercongruences for ordinary primes. The other method makes use of the theory of hypergeometric motives, in particular, adapts the techniques from the recent work of Beukers, Cohen and Mellit on finite hypergeometric sums over $\mathbb Q$. Essential ingredients in executing the both approaches are the modularity of the underlying Calabi--Yau threefold and a $p$-adic perturbation method applied to hypergeometric functions.

This is a joint project with Fang-Ting Tu, Noriko Yui, and Wadim Zudilin.


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