Generators are essential to understand any algebraic structure and triangulated categories are no different. In this half(?) of the talk, we discuss joint work with Pat Lank where we show that higher iterated pushforwards of the category perfect complexes under Frobenius generates the bounded derived category of a Noetherian F-finite scheme over a field of prime characteristic.
We discuss a general proposal (or grand unified theory) for associating integral kernels to flips due to myself, Colin Diemer, and David Favero.
We focus on recent joint work with Nitin Chidambaram and David Favero where this construction is used to obtain Fourier-Mukai kernels for stratified Mukai flops.
This is a talk I gave at the Banff International Research Station for the workshop Derived Categories, Arithmetic, and Reconstruction in Algebraic Geometry.
As I couldn't choose a single topic, I decided to try a double feature. Perhaps it was doubly opaque.
The presentation uses the Reveal.js framework, the KaTeX engine to render math, and is hosted with GitHub Pages.
Reveal.js comes with server which hot reloads on changes to the html files. If you don't have your own server, I recommend using this.
To use this as template for your talk, first install node. The simplest way for an up-to-date version is via nvm. Then install npm.
Next, clone this repository. Inside the main folder of the repository, run
npm install to build the node module dependencies.
Run npm start to initialize the server. It will provide a url address for the server.
Now edit index.html to author your talk and point your favorite browser to
the url to see the results.
To enable access via the internet, set up GitHub Pages.