Autumn 2026

8 Oct 2026

Jeremy Alm 

The Most Wanted Folkman Graph Is Still At Large

Abstract:  Any red-blue coloring of the edges of $K_6$, the complete graph on six vertices, must contain a monochromatic triangle.  As a corollary, any red-blue edge coloring of a graph $G$ with clique number at least six must contain a monochromatic triangle as well.

One may ask if "six" is strictly necessary in the above statement. In other words, are there graphs with clique number smaller than six, that still have the forced-monochromatic-triangle property?  (Spoiler: Yes, there are!) We will explore such graphs and stumble all the way to a stubborn open problem. Bellicose debate will follow. 

FALL 2026

1 Oct 2026

Mathew Gluck

Introduction to cellular sheaves and the cellular sheaf Laplacian

Abstract: The cellular sheaf Laplacian over a graph generalizes the usual graph Laplacian. I will give an accessible introduction to cellular sheaves and the corresponding Laplacian. 

FALL 2026

24 Sep 2026

Jerzy Kocik

Introduction to harmonic evolutions on graphs 

Keywords: graph theory, evolutions, boundary, coboundary, Laplacian, proto-physics

Source (pdf)  Video (YT)

FALL 2026

3, 10, 17 Sep 2026

Mathew Gluck

Bifurcation results for nonlinear problems involving the graph Laplacian 

Recording of Part 1

Recording of Part 2

Recording of Part 3

Abstract: This note illustrates some standard bifurcation results in nonlinear functional analysis in a setting that welcomes those with no experience in functional analysis. Specifically, I will show that for a suitable family of nonlinear PDEs involving the graph Laplacian on a finite connected simple graph, the first eigenvalue of the graph Laplacian is a bifurcation point. Moreover, there is a smooth parameterized curve of nontrivial solutions bifurcating from the trivial solution at the first eigenvalue.

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.

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.