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Home >> Seminar

Supercongruences for Rigid Hypergeometric Calabi—Yau Threefolds

Prof. Long Ling(龙玲 教授)
Saturday, May 27th, 2017, 10:00 AM  闵行数学楼102室
龙玲博士现在是美国路易斯安那州立大学数学系教授,她1997年在清华大学获得数学学士学位,2002年在美国宾夕法尼亚州立大学获得数学博士学位。龙玲教授的主要研究领域是数论和模形式理论。她在这些领域取得了许多重要的研究成果,曾获得2012-2013年度 AWM Michler 纪念奖。 迄今她已经在Mathematische Annalen, Trans. Amer. Math. Soc, Adv. in Math 等著名刊物上发表了30多篇学术论文。

We establish the supercongruences for eleven remaining of the fourteen rigid Calabi--Yau threefolds over Q of hypergeometric type, conjectured by Rodriguez-Villegas in 2003. Two different approaches are used. One is based on Dwork's theory of p-adic unit roots, which allows us to prove the supercongruences for ordinary primes. The other approach is based on the theory of hypergeometric motives. In the latter case, we adapt recent work of Beukers, Cohen and Mellit on finite hypergeometric sums over Q, and use p-adic analysis. This is a joint work with Fang-Ting Tu, Noriko Yui, and Wadim Zudilin.

主持人:刘治国 教授
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