Abstract. In this talk we will look at various examples of classification problems in symplectic linear algebra: conjugacy classes in the symplectic group and its Lie algebra, linear lagrangian relations up to conjugation, tuples of (co)isotropic subspaces. I will explain how many such problems can be encoded using the theory of symplectic poset representations, and will discuss some general results of this theory. Finally, I will recast this discussion from a broader category-theoretic perspective.
Here are some papers to read for more detail:
• Jonathan Lorand, Classifying linear canonical relations.
• Jonathan Lorand and Alan Weinstein, Decomposition of (co)isotropic relations.
Lorand is working on a paper with Weinstein and Christian Herrman that delves deeper into these topics. I first met him at the ACT2018 school in Leiden, where we worked along with Blake Pollard, Fabrizio Genovese (shown below) and Maru Sarazola on biochemical coupling through emergent conservation laws. Right now he’s visiting UCR and working with me to dig deeper into these questions using symplectic geometry! This is a very tantalizing project that keeps on not quite working…