
Combinatorics/Algebra Seminar
The seminar is meeting most Mondays at 4:10 pm CDT in 401 Carver Hall.
If you wish to invite a guest or give a talk, please visit the
Post Office.

March 27

Cody Fleming (Mechanical Engineering, ISU): Categorical semantics of cyberphysical systems theory.
Abstract:
Cyberphysical systems (CPS) require the construction and
management of various models to assure their correct, safe, and secure
operation. I will first describe CPS applications and the various
formalisms present in current CPS research. Unfortunately, to date the
different model views of cyberphysical systems are disparate and
largely related informally, which raises issues with the degree of
formal consistency between those various models of requirements, system
behavior, and system architecture. I will present a categorytheoretic
framework that makes different types of composition explicit in the
modeling and analysis of cyberphysical systems, which assist in
verifying the system as a whole. In particular, I will focus on modeling
system behavior via algebras on the monoidal category of wiring
diagrams, system requirements (e.g. on safety) again as an algebra on
certain objects in this monoidal category, and the CPS design process
using the notion of a slice category.

March 20: no seminar.

March 13: Spring break.

February 27, March 6

Connor Depies: Generalizing the octonions with trilinear forms.
Abstract:
The quaternions can be created using a symmetric bilinear form on the real vector space spanned by i and j. We then generalize by changing the bilinear form to get other structures; e.g., the split quaternions and the exterior algebra of 4 dimensions. Such generalizations give us Clifford algebras. We generalize the octonions in a similar manner, but nonassociativity requires that in addition to a symmetric bilinear form, we need an antisymmetric trilinear form. We study these generalizations using a vector space of three dimensions, obtaining eightdimensional algebras, and present some particular examples.

February 20: no seminar.

February 6, 13

Justin Stevenson: An introduction to covering quasigroups.
Abstract:
In the first talk I will introduce the idea of a covering quasigroup, and present a proof of their existence which is due to Hilton and Wojciechowski. We will show how these covering quasigroups can be used to get an analogue of the character group that works in the nonabelian group case. In the second talk I will discuss the metacyclic groups, their characters, and what their covering quasigroups look like.

January 23, 30

Jonathan Smith: Catalan numbers, convex polytopes, and Fermat curves.
Abstract:
Catalan numbers count the number of possible ways to parse a nonassociative product. In these talks (reporting joint work with A. Romanowska, A. ZamojskaDzienio, and L. Long), we discuss two of the many places where Catalan numbers show up: in the decomposition of convex polytopes, and in the numbertheoretical study of Fermat curves.
Archive of earlier seminars
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