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Seminar on periods and motives | Differential equations, hypergeometric families, and Beilinson's conjectures

来源: 05-27

时间:Tuesday, 9:00-10:00 am May 28, 2024

地点:Zoom Meeting ID: 687 513 9542 Passcode: YMSC

组织者:Jin Cao (THU), Ma Luo (ECNU)

主讲人:Matt Kerr Washington University in St. Louis

Abstract:

We discuss two approaches to solving inhomogeneous equations of the form L(.)=t^{1/d}, where L is a hypergeometric differential operator attached to a family of CY varieties. The first is by elementary complex analysis, using so-called Frobenius deformations, and gives an explicit series solution. The second is via normal functions attached to algebraic cycles (both "classical" and "higher") on a base-change of the family.

I will briefly review regulator maps, their relation to inhomogeneous Picard-Fuchs equations, and the relevant cases of the Beilinson conjecture. Turning then to the CY3 examples classified by Doran-Morgan, I will explain how to identify which types of cycles arise (viz., K_0, K_2, or K_4 classes), and how to use the Frobenius deformations to make the conjecture more explicit. This is joint work with Vasily Golyshev.

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