2023 Section Meeting

Invited talks

David Richeson, Dickinson College

A Romance of Many (and Fractional) Dimensions

Abstract: Dimension seems like an intuitive idea. We are all familiar with zero-dimensional points, one-dimensional curves, two-dimensional surfaces, and three-dimensional solids. Yet dimension is a slippery idea that took mathematicians many years to understand. We will use pictures, animations, and analogies to describe our three dimensions and help us visualize a fourth dimension. We will discuss the history of dimension, the public's infatuation with the fourth dimension, time as an extra dimension, the meaning of non-integer dimensions, and the unexpected properties of high-dimensional spaces.

Haydee Lindo, Harvey Mudd College

Looking for the Center

Abstract: Do you know which matrices commute with all the others? Do you know a beautiful structural algebraic reason behind the answer? The well-known trace map on matrices can be generalized to a map on any module over a commutative ring. The image of such a map is called a trace ideal. I will speak on some recent developments in the theory of trace ideals with applications to our understanding about the relationship between modules, rings and ideals. Ultimately, this will help us understand the commutative centers of endomorphism rings.

Deirdre Longacher Smeltzer, MAA Senior Director for Programs

Invariants and Monovariants: Can I get there from here?

Abstract: Many games and puzzles consist of attempting to change a given configuration from one state to another using a prescribed set of permissible moves. Interesting mathematics arises from asking questions such as "Can Player 1 beat Player 2 in six moves?" and "Can a 10 x 10 square grid be tiled with 25 copies of a 1 x 4 tile?" The notions of invariants (that is, properties that remain fixed when moving from one permissible state to another) and monovariants (properties that change monotonically when moving from one permissible state to another) can often be utilized to provide a clever solution to such questions.