Abstracts 

Eugenie Hunsicker (Loughborough University) : Architecture for the Working Mathematician 

Architecture Definition is the process in systems engineering of developing an architectural structure appropriate for achieving a given set of system requirements and constraints. Last winter, I was contacted by a colleague from systems engineering interested in developing a mathematical formalism for defining architecture, classifying architectures and comparing architectures. What emerged uses a combination of model theory from logic and category theory. I will talk about this work, as well as the occasionally surreal experience of collaborating with systems engineers, whom it transpires are even more obsessed with precision of language than mathematicians and walk a line between abstract philosophy and practical engineering. 

Louis Theran (University of St. Andrews): Graph rigidity and measurement varieties

Geometric rigidity theory is concerned with how much information about a configuration p of n points in a d-dimensional Euclidean space is determined by pairwise Euclidean distance measurements, indexed by the edges of a graph G with n vertices. One can turn this around, and, define, for a fixed graph G, a “measurement variety" associated with all possible edge lengths measurements as the configuration varies. I’ll survey some (somewhat) recent results in geometric rigidity obtained by studying the geometry of measurement varieties. 

Jeffrey Giansiracusa (Swansea University): Tropical differential equations

Grigoriev introduced a theory of tropicalizing differential equations and their formal power series solutions over a trivially valued field.  I will describe some generalizations of this theory and what kinds of information they are capable of detecting.  In particular, I will explain how to extend to non-trivially valued coefficients and broader classes of series solutions, as well as a variation adapted to studying positive real solutions.

Sponsors:

We are grateful for the financial support from the Glasgow Mathematical Journal Learning and Research Support Fund, from the Edinburgh Mathematical Society,  the London Mathematical Society.