This is the first talk in a two part series, where the ultimate goal is to discuss some positivity conjectures in the ring of symmetric functions.
Symmetric functions and their variations are fundamental examples of combinatorial Hopf algebras. The first talk gives a short introduction to these algebras with the underlying motivation of preparing for combinatorial positivity questions. For important context, we will also discuss some related Hopf algebras: quasisymmetric functions and noncommutative symmetric functions.
(+)symmetric functions as combinatorial Hopf algebras
A Stone space is a compact, totally disconnected, Hausdorff space. In model theory, Stone spaces naturally arise as spaces of complete types of a structure. Various model theoretic properties will be controlled by the topological properties of these spaces. In this talk, we will define model theoretic "types" and their associated Stone space structure. For the purpose of better understanding Stone spaces, we will also present Stone's Duality Theorem, as well as a more general duality theorem due to Hu.
https://cuboulder.zoom.us/j/97617189995
Stone Spaces
Sep. 13, 2022 11pm (Math 350)
Number Theory
David Grant (University of Colorado Boulder)
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This is to get us started on our mini study group on the role of genus 2 curves and abelian surfaces in breaking SIDH/SIKE, the isogeny-based cryptography scheme (that was spectacularly broken a month ago). David has kindly offered to give us an overview on genus 2. All are welcome.
(+)symmetric functions as combinatorial Hopf algebras