This is the homepage of the Algebra and Algebraic Geometry Seminar at McMaster University. This seminar is primarily intended for McMaster University graduate students, postdocs, and faculty with an interest in algebra, algebraic geometry, number theory, or related areas. If you are interested in giving a talk, please contact one of the faculty members affiliated with the seminar: Cam Franc, Megumi Harada, Jenna Rajchgot, or Adam Van Tuyl,
During Fall 2025, talks take place Tuesdays at 11:30-12:20am (Eastern) at HH 312.
Let E be an elliptic curve over the rationals given by an integral Weierstrass model and let P be a rational point of infinite order. The multiple nP has the form (A_n/B_n^2,C_n/B_n^3) where A_n, B_n, C_n are integers with A_nC_n and B_n coprime, and B_n positive. The sequence (B_n) is called the elliptic divisibility sequence generated by P. In this talk we answer the question posed in 2007 by Everest, Reynolds and Stevens: does the sequence (B_n) contain only finitely many perfect powers?
We discuss (mostly) recent work from several authors on epsilon and Hilbert Kunz multiplicities.
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds over algebraically closed fields is a notoriously difficult problem. In contrast to the situation in lower dimensions, rank 2 bundles over smooth affine fourfolds are no longer uniquely determined up to isomorphism by their Chern classes. In this talk, we survey classification results in low dimensions and analyze the cohomological obstructions for the set of isomorphism classes of rank 2 bundles with prescribed Chern classes over a fixed smooth affine fourfold to be finite (resp. a singleton). This enables us in many cases to enumerate isomorphism classes of rank 2 bundles with prescribed Chern classes; we can even completely classify rank 2 bundles over some concrete smooth affine fourfolds. The talk is based on joint work with Thomas Brazelton and Morgan Opie.