Algebraic, Geometric, and Topological Methods in Optimization

Topological Methods in Algebraic Geometry

Preface These are live-texed lecture notes for a course taught in Cambridge during Michaelmas 2013 by Burt Totaro, on a hodgepodge of topics at the intersection of algebraic topology and algebraic geometry. An unfortunate side effect of live-texing is that it tends to introduce a lot of errors, which are solely the fault of the scribe. If you find any, please let me know at

Optimization in Algebraic and Topological Vector Spaces

Topological and Geometric Methods in Qft

These notes were taken at the NSF-CBMS conference on topological and geometric Methods in QFT at Montana State University in summer 2017. Most of the lectures were given by Dan Freed. I live-TEXed these notes using vim, and as such there may be typos; please send questions, comments, complaints, and corrections to [email protected]; any mistakes in the notes are my own. Thanks to Nilay K...

Geometric and Topological Methods in Concurrency Theory

Inmodern computers (or computer networks), calculations are typically no longer perfomed sequentially (one step at a time) but in cooperation between several processors doing parts of the job in parallel. Through concurrency, one aims to save time and memory. To do so, the proper scheduling of processors is a crucial task. Some of the issues involved are to make sure that the calculation does n...

Algebraic and geometric methods in enumerative combinatorics

Enumerative combinatorics is about counting. The typical question is to find the number of objects with a given set of properties. However, enumerative combinatorics is not just about counting. In “real life”, when we talk about counting, we imagine lining up a set of objects and counting them off: 1, 2, 3, . . .. However, families of combinatorial objects do not come to us in a natural linear ...