MATH Seminar
| Title: Local-global principles on stacky curves and solving generalized Fermat equations |
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| Seminar: Algebra |
| Speaker: Yidi Wang, PhD of University of Western Ontario |
| Contact: Deependra Singh, deependra.singh@emory.edu |
| Date: 2025-02-18 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The primitive solutions of certain generalized Fermat equations, i.e., Diophantine equations of the form Ax^2+By^2 = Cz^n, can be studied as integral points on certain stacky curves. In a recent paper by Bhargava and Poonen, an explicit example of such a curve of genus 1/2 violating local-global principle for integral points was given. However, a general description of stacky curves failing the local-global principle is unknown. In this talk, I will discuss our work on finding the primitive solutions to equation of the form by studying local-global principles for integral points on stacky curves constructed from such equations. The talk is based on a joint project with Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin, Manami Roy, and Soumya Sankar. |
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