James Mahoney, Portland State University

*Pattern or coincidence?: The strong law of small numbers*

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Broad areas of mathematics are devoted to discovering, describing, and proving the existence of patterns.
Sometimes the general formula for a pattern can be produced after observing just a few terms.
Conversely, sometimes a pattern holds for a very long time before a counterexample rears its head.
In this talk I will present to you a plethora of "patterns" that arise from peculiar places.
Your job will be to decide whether a pattern truly exists or if what you see is just a coincidence.
This is a great opportunity to test your mathematical intuition as well as to see some interesting problems.
Answers and explanations will be provided at the end, and there is a prize!

Elise Lockwood, Oregon State University

*Rook polynomials as a unifying combinatorial concept*

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Some problems in combinatorics and graph theory can be modeled in terms of ways to place non-attacking rooks on a chessboard.
The theory behind such problems involves rook polynomials, and there a number of topics that rook polynomials can exemplify and unify in an interesting (and fun!) way.
In this talk, we explore the topic of rook polynomials, emphasizing their accessible yet powerful nature.

James Mahoney, Portland State University

*Growing our understanding of tree graphs*

Through definitions, examples, and pictures, in this accessible talk I will share the latest research on tree graphs.
I’ll explain what tree graphs are, what properties they have, and why they’re such fascinating mathematical objects.