Calendar

We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate’s thesis. We then propose a genus one p-adic string worldsheet action. The key is the definition of a p-adic Laplacian operator on the Tate curve. We show that the genus one p-adic Green’s function exists, is unique under some obvious constraints, is locally constant off diagonal, and has a reflection symmetry. It can also be numerically computed exactly off the diagonal, thanks to some simplifications due to the p-adic setup. Numerics suggest that at least in some special cases, the asymptotic behavior of the Green’s function near the diagonal is a direct p-adic counterpart of the familiar Archimedean case, although the p-adic Laplacian is not a local operator. Joint work in progress with Rebecca Rohrlich.

A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized and applied in many directions. It also struck a fresh wave of interest in finite Ramsey theory. Many classes of finite structures are shown to have the Ramsey property by encoding their problem in a known Ramsey class and translating a solution back. This is often a case-by-case approach and naturally there is a great need for abstracting the process. There has been much success on this front, however, none of the tools captures every situation. We will discuss one such encoding via a model-theoretic notion of semi-retraction introduced by Lynn Scow in 2012. In a joint work, we showed that a semi-retraction transfers the Ramsey property from one class of structures to another under quite general conditions. We compare semi-retractions to a category-theoretical notion of pre-adjunction revived by Mašulović in 2016. If time permits, I will mention a transfer theorem of the Ramsey property from a class of finite structures to their uncountable ultraproducts, which is an AIMSQuaRE project with Džamonja, Patel, and Scow.