Title of Oral/Poster Presentation

Exterior Products of Linear PDEs and Geometry of Calabi-Yau manifolds

Class

Article

College

College of Science

Faculty Mentor

Andreas Malmendier

Presentation Type

Oral Presentation

Abstract

Given two linear differential equations of finite rank (i.e., the dimension of the solution space) defined on the same space, one may define their tensor product, symmetric product, and exterior product. In this talk, I will discuss a 3-parameter rank-5 system of linear partial differential equations that arises from the exterior product of the connection forms of two Pfaffian systems; this differential system governs the periods of the Jacobian of a generic smooth genus-two elliptic curve. I will explain the connection of this differential system to the Picard-Fuchs system of a family of lattice polarized K3 surfaces of Picard-rank 17.

Location

Room 154

Start Date

4-12-2018 9:00 AM

End Date

4-12-2018 10:15 AM

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Apr 12th, 9:00 AM Apr 12th, 10:15 AM

Exterior Products of Linear PDEs and Geometry of Calabi-Yau manifolds

Room 154

Given two linear differential equations of finite rank (i.e., the dimension of the solution space) defined on the same space, one may define their tensor product, symmetric product, and exterior product. In this talk, I will discuss a 3-parameter rank-5 system of linear partial differential equations that arises from the exterior product of the connection forms of two Pfaffian systems; this differential system governs the periods of the Jacobian of a generic smooth genus-two elliptic curve. I will explain the connection of this differential system to the Picard-Fuchs system of a family of lattice polarized K3 surfaces of Picard-rank 17.