Talk Math With Your Friends
Talk Math With Your Friends (TMWYF) is a weekly virtual mathematics colloquium. The speaker will present for 45 minutes, followed by 15 minutes of questions and discussion. Talks will be recorded and posted, subject to the consent of the speaker.
Click the button below to join us live via Zoom each Thursday from 3:30-4:30 Eastern (12:30-1:30 Pacific). More information is on our Zoom Info page.
May 27, 2021 3:30-4:30 Eastern (12:30-1:30 Pacific). Brendan Sullivan, Emmanuel College
Product Graphs and the Chaser-Runner Game
Pursuit-evasion games on graph networks have been investigated for decades. The classic "cop and robber" game was introduced in the 1980s (Nowakowski & Winkler) and has since spawned many interesting results and conjectures, as well as several variations on the basic rules. In this presentation, I plan on discussing two kinds of graph products: the Cartesian product and the strong product. We will see how they can make interesting graphs on which to play the game, as well as how they play starring roles in some algorithms that can computationally determine the "cop number" and "capture time" of a graph. Finally, this talk will also be an attempt to promote "chasers vs. runner" (or any better suggestions you have!) as more appropriate terminology for this game.
Stay tuned for updates!
Most Recent Talk
May 6, 2021 3:30-4:30 Eastern (12:30-1:30 Pacific). Carol Jacoby, Jacoby Consulting
The Liar’s Paradox and the Foundations of Mathematics
The Liar’s Paradox, stated most directly as, “This sentence is false,” was around as a puzzle and curiosity for over 2000 years. Then variants of it caused crises in the modern foundations of mathematics. First, Russell’s Paradox forced mathematics to rethink the concept of sets that underlies it all. Then Kurt Gödel proved that the holy grail of mathematics—a complete axiomatization of mathematics--was impossible. In particular, no matter how sophisticated your mathematical machinery, there will always be true statements that cannot be proved. This holds even if you restrict yourself to arithmetic. We will discuss these paradoxes and how they changed mathematics. We will outline Gödel’s ingenious proof and reflect on what it tells us about mathematics.