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.

2 April

Annie Vargas Lizarazo 

Gradient refractive indices enable squid structural color and inspire multispectral materials

Spring 2026

 

19 and 26 March

John McSorley

Special and super graph special subgraphs of a graph 

Spring 2026

5 March

Philip Feinsilver

Leverrier-Faddeev and a basic recursion

Video

Abstract: The method of synthetic substitution in elementary algebra is the basis of an elegant method presented by the astronomer Leverrier to find the characteristic polynomial of a matrix without evaluating determinants.

Spring 2026

26 Feb 2026

Jakson Lewis

Observations on Representations of Lie Algebras via Harmonic Oscillators

Abstract: We present the method of representing Lie Algebras with the use of the algebra of Harmonic Oscillators, and with that present an interesting challenge and interesting results discovered from such investigations. 

Spring 2026

From arstexnica

12 and 19 February

Mohammad Sayeh

Nobel AI

Mike Sullivan shares with you two books that he read on the history of AI/machine learning:

• What is ChatGPT Doing …and Why Does it Work (by Stephen Wolfram)
• Why Machines Learn (by Anil Ananthaswamy)

(From Mohammad: see also Hopfield's early work:  1982Hopfield ,  1984Hopfield, 1985Hopfield, 1986Hopfield ).

Spring 2026

5 February

Ronald White

An introduction to non-associative algebra

Abstract:   In this talk, we begin by introducing some of the more common non-associative operations and showing how we use them in everyday contexts. We then move into algebraic structures, starting with a magma, a set that is simply closed under a single binary operation. From there, we gradually impose additional structure until we arrive at loops, which can be thought of as groups that are not necessarily associative. This is where we will spend the remainder of our time, exploring what these structures contribute to our understanding of groups and what questions we can study about them in their own right.

SPRING 2026

22 and 29 January

Jerzy Kocik

A group, an application, a puzzle, and an analog toy

(moduli space of Apollonian disk packing via the bimodular group)  

Autumn 2025

René Magritte, "This is Not a Pipe."

4 December 

Leonard Fowler

Math and not-Math

Autumn 2025

20 November 

Mohammad Sayeh

Future before Now:  anticipatory (proteretic) structure

Autumn 2025

30 October, 6 and 13 November

Jackson Lewis

Hyperbolic Angular Momentum from the ground up

Abstract:  We present the construction of “hyperbolic angular momentum” as given by Schwinger (1951), starting with the basic one-dimensional oscillator of classical mechanics. Then we introduce harmonic oscillators in quantum mechanics, angular momentum in classical and quantum mechanics, and the Jordan-Schwinger Map. Some applications will be discussed, possibly including constructions of spin networks and discrete spacetime operators in loop quantum gravity.  

From "Math for Poets..."

16, 23  Oct 2025

Mathew Gluck

The Method of Moving Spheres

Abstract. The method of moving spheres is a powerful and versatile method for analyzing partial differential equations with conformal symmetry. At the core of this method is the amazing fact that one can classify all suitably nice functions f  defined on Euclidean space for which both of the following properties hold:

1.  For every point x there is a sphere centered at x about which f  has inversion symmetry, and

2.  for every direction e, there is a hyperplane with normal direction e about which f  has reflection symmetry.

I will give some examples of functions for which both properties hold, and I will discuss the historical development of the classification of all such functions. Finally, I will overview the method of moving spheres and provide some applications of the method in the analysis of conformally covariant partial differential equations.

Autumn 2025

3 and 10  October

Viska Arbogast

Numbers as Equations

Autumn 2025

 

From Wikipedia

11, 18, 25  Sep 2025

Jerzy Kocik

Coxeter groups, and an unconventional view on the unimodular group (with pictures)

Part 1:  Coxeter groups (the idea)

Part 2:  Modular group as a Coxeter group

Part 3:  "Supermodular" group and an unexpected application 

For part 1, you may consult a nicely written text by J. Baez:  Coxeter and Dynkin diagrams. 

From Nature Reviews Physics 1,437-449 (2019)

5 Dec, Thursday, 1pm

Ines Cavero-Pelaez
University of Zaragoza, Spain

About the geometrical phase

Video

Autumn 2024

21 Nov 2024

Stacey Staples

Spectral Properties of the Zeon Combinatorial Laplacian

Video

Autumn 2024

7 and 14 Nov, Thursday

Jerzy Kocik

A certain expansion (evolvement) of ${\rm SL}(2,\mathbb Z)$ and its role as the symmetry group of the Apollonian "time crystal."

Autumn 2024

The art from here

24 and 31 Oct, Thursday

Philip Feinsilver

Convergence theorems for matrices with some negative entries

See the outline.

Video:  Part 1 and Part 2