### ε-series by Corrine Yap, Jing Yu, and Changxin Ding

- Series
- Graph Theory Seminar
- Time
- Friday, March 8, 2024 - 15:15 for 1 hour (actually 50 minutes)
- Location
- Skiles 308
- Speaker
- Corrine Yap, Jing Yu, and Changxin Ding – Georgia Tech

Corrine Yap: The Ising model is a classical model originating in statistical physics; combinatorially it can be viewed as a probability distribution over 2-vertex-colorings of a graph. We will discuss a fixed-magnetization version—akin to fixing the number of, say, blue vertices in every coloring—and a natural Markov chain sampling algorithm called the Kawasaki dynamics. We show some surprising results regarding the existence and location of a fast/slow mixing threshold for these dynamics. (joint work with Aiya Kuchukova, Marcus Pappik, and Will Perkins)

Changxin Ding: For trees on a fixed number of vertices, the path and the star are two extreme cases. Many graph parameters attain its maximum at the star and its minimum at the path among these trees. A trivial example is the number of leaves. I will introduce more interesting examples in the mini talk.

Jing Yu: We show that all simple outerplanar graphs G with minimum degree at least 2 and positive Lin-Lu-Yau Ricci curvature on every edge have maximum degree at most 9. Furthermore, if G is maximally outerplanar, then G has at most 10 vertices. Both upper bounds are sharp.