An obstruction to weak approximation on a Calabi-Yau threefold

Abstract: In this talk, we investigate the arithmetic structure of a class of Calabi-Yau threefolds. These threefolds were constructed over the complex numbers by Hosono and Takagi as a linear section of a double quintic symmetroid, and have a beautiful and simple story in the geometry of quadrics over the rational numbers. In forthcoming work with Honigs, Lamarche, and Vogt, we exhibit an obstruction to weak approximation on these threefolds. For the "experimental" nature of this seminar, we will conclude by working through a demonstration in cocalc. Attendees are asked to make cocalc accounts to participate fully; no prior coding experience necessary!

commutative algebraalgebraic geometrynumber theory

Audience: learners

Experimental Talks in Algebraic Geometry

Series comments: Description: Exploring ways to virtually communicate math

The recent shift from in-person to online talks provides us with an opportunity to explore new and interesting ways to communicate and learn things related to algebraic geometry. The goal of this seminar is to provide a space for speakers and audience members to do this exploration.

Each speaker will be given 50 minutes to create and lead an environment where topics related to algebraic geometry can be communicated and learned. How the speaker uses their time and creates such an environment is entirely up to them. They may try mixing pre-recorded and live aspects of a talk, they might try leading group work, who knows, it is entirely up to the speaker. The only request made of speakers is that they think critically about new ways to best use their time to promote the communication and learning of math. After the 50 minutes, a short group discussion will be held discussing how this form of online math communication went, and how it might be built upon. Everyone participating is asked to keep in mind that this is a place for experimentation.

This event is being organized by Juliette Bruce in association with the Algebraic Geometry Syndicate (AGS) discord server. Updates about the talks will be posted both here and on the AGS discord server. If you would like to join the AGS discord server please email juliette.bruce 'at' math.wisc.edu.