Abstract: Through the universal $G$-space $EG$, once can replace a $G$-space $X$ by a homotopy equivalent space in which the $G$-action is free. the orbit space of this action is the Borel construction. This Borel construction is then a better model to study the $G$-action, as not only can we use tools of algebraic topology such as cohomology (which leads to equivariant cohomology) and spectral sequences, but also computations using these tools are often way nicer.

Meeting ID: 997 4840 9440 Passcode: 911104

Abstract: We will discuss how to compute dynamical invariants of a surjective endomorphism of a projective bundle over an elliptic curve. This has applications to arithmetic dynamics and the Kawaguchi-Silverman conjecture. In particular, we will discuss how to use the theory of Schur functors to compute the Iitaka dimension of certain projective bundles. This extends work done by Atiyah in classifying vector bundles on elliptic curves.