Spring 2026

Escher, from Wiki

30 April

Layla Sorkatti

A First Look at Symplectic Alternating Algebras

Abstract.  Let F be a field. A symplectic alternating algebra over F is a triple (V, ( , ), ⋅ ), where V is a symplectic vector space over F with respect to a non-degenerate alternating form ( , ),  and ⋅ is an alternating bilinear operation on V such that the identity (u⋅v,w) = (v⋅w, u) holds.

In this talk, we will present these algebras in their own right from an algebraic perspective. The aim is to provide an overview of topics that can be explored in detail in future talks.

Spring 26

From Cantor's Paradise

23 April 2026

Leonard Fowler

Relevant vector spaces: some mathematics for aliens

Abstract: A relevant logic is one for which one cannot go from arbitrary premises to some unrelated conclusion. In this talk, we'll look at models of the usual vector spaces over the rational numbers, but where we change the logic we are reasoning with/ which furnishes the models we work with. While leading to some perhaps unnatural objects, they might still be of some legitimate mathematical interest, if only in what mathematics could (or could have) looked like.  

From Wikipedia (fragment)

16 April
 
Tevian Dray

Oregon State University

Using Division Algebras to Describe Symmetry, with Applications to Physics

Abstract:  Quaternions are often used to describe rotations in 3 (Euclidean) dimensions.  Several generalizations of this fundamental idea will be discussed, notably the extension to the octonions and the inclusion of spinor transformations as well as vector rotations.  The symmetry groups described by the resulting framework include the Lorentz group in 3, 4, 6, and 10 (spacetime) dimensions, which are precisely the dimensions in which classical supersymmetry holds.  This framework culminates in the well-known Tits-Freudenthal magic square of Lie algebras, providing a unified treatment of the exceptional Lie groups.  Some applications of particle physics will be briefly mentioned if time permits.

Spring 2026

17 April

Seth Lawence

The Physics of Society: A Geometric Framework for Social Consequences

Abstract: Carlo Cipolla’s classification of human behavior organizes actions by their outcomes for the actor and others. In this talk, we reinterpret this plane as a geometric representation of relationships between agents, where each action is a point defined by its evaluated outcomes.

This perspective reveals a natural decomposition of actions into total outcome and its distribution, leading to a coordinate transformation that separates these effects. Under changes of point of view, the total outcome remains invariant while the distribution reverses, exposing a symmetry structure underlying social interactions.

These results point to a broader geometric framework in which relationships form networks and suggest a form of social relativity.