A convoluted situation: fine-grained algorithms and complexity through the lens of min-plus convolution

In recent years, various approaches to combinatorial problems have entered the fine-grained toolbox. Min-plus convolution is one such problem that plays a central role in this development. I will present an overview of the diverse techniques that have emerged through this problem. This includes conditional lower bounds, P-in-FPT, polyhedral optimization and extension complexity. This talk is based on joint work with Cornelius Brand and Martin Koutecký.