# Spring 2024 (Current Semester)

The colloquium meets on Thursdays at 2:40pm, unless otherwise stated.

• February 29th

The Carpenter’s Rule Problem

Is it possible to take any given polygon and move it through space to a convex polygon, while never having the polygon intersect itself? If you drop a necklace on a flat table and attempt to do this yourself, you’ll probably be able to successfully do this. This is far from a mathematical proof, however, and this problem, known as the Carpenter’s Rule Problem, remained open for decades until it was solved in the early 90s. In this talk, I’ll introduce the Carpenter’s rule problem and explain a surprising approach for how to solve it that involves an important technique in optimization known as linear programming. Most of this talk should be approachable for anyone who enjoys looking at pictures and has taken a calculus course. [flyer]

• March Canceled

Canceled

• April 25th

Uniquely Completable Partial Latin Squares

A latin square of order $n$ is an $n \times n$ array in which each symbol from a set of order $n$ appears exactly once in each row and exactly once in each column. If we loosen the definition so that each symbol appears at most once in each row and at most once in each column (and so there may be empty cells) then we have a partial latin square. A partial latin square is uniquely completable if there is exactly one way to fill in the empty cells to obtain a latin square.

We look at some historical and recent work related to uniquely completable partial squares. Motivating questions include: how few entries can a uniquely completable partial latin square have? How many can one have, if it is minimal in the sense that removing any entry allows multiple completions? What if we add extra conditions (like a sudoku puzzle does)? Does it make sense to ask about infinite latin squares? There are many accessible open problems.

Includes joint work with Aurora Callahan, Emma Hasson, Kaethe Minden and Yolanda Zhu. [flyer] [slides]