We will continue David's exposition on genus 2 curves and isogenies of their Jacobians.
Genus 2 curves and isogenies of their Jacobians
Sep. 20, 2022 2:30pm (MATH 3…
Lie Theory
Nat Thiem (CU)
X
Stanley associated a symmetric function to each finite graph in such a way that the function encodes proper vertex colorings on that graph. The s-positivity and e-positivity of these functions has been of great interest in recent years, especially since neither positivity is even true for all graphs. For unit interval graphs we know s-positivity and e-positivity is conjectured. This talk translates these conjectures into representation theoretic questions in the framework of combinatorial Hopf algebras.
Stanley chromatic symmetric functions and positivity conjectures
Sep. 20, 2022 3:30pm (MATH 3…
Topology
Howy Jordan (CU Boulder)
X
By interpreting theories in categories other than set, we recover completeness theorems from finitary logic in an infinitary setting. Topoi, categories of sheaves, have enough structure to interpret large classes of theories, and we obtain notions of local truth. A sheaf of rings on a sober space X gives for instance a ring object in Sh(X) and this ring is a local ring iff each germ is a local ring. In this talk, we set up the notion of interpreting a theory's axioms in a topos. We also consider consequences for the reals and some algebraic structures.