In Summer 2023, group meetings will take place at 2 PM Pacific Time on Wednesdays in Academic Surge 2022 (for in-person attendees) or on Zoom (for remote attendees, see group Slack for link). All regular meetings are recorded and uploaded to our meeting archive on Box and previously on Dropbox. Members Name Institution Program Research interests Isaac Kim UC Davis

:::danger Last update: 8/30/2021, Isaac Kim Unfortunately, this line of approach seems to be too restrictive; see the last section for the underlying reason. Therefore, the notion of extremality, at least the one defined in this document, does not seem like a promising approach. Nevertheless, this document is left as is because there are some interesting concepts introduced here. Some of those concepts may be migrated to a separate note in the future. ::: Consider a quantum spin system arranged on $\mathbb{R}^2$. We can partition $\mathbb{R}^2$ into a set of $2$-cells, $1$-cells, and $0$-cells. Each $2$-cell and $1$-cell is homeomorphic to a disk and an open interval, respectively. The $0$-cells are points. In the figure below, a $2$-cell is represented by a red cell, a $1$-cell is represented by a blue line, and a $0$-cell is represented by a green dot.