Just wrapping up my second week at the Banff International Research Station. This week's workshop is on Statistics and Machine Learning. The highlight, for an outsider like me, has definitely been Tselil Schramm's mini-course on the sum-of-squares algorithmic paradigm. A decade's worth of research nicely condensed into four one-hour lectures.
An implementation of the Product Structure Theorem for planar graphs, in Python:
Not exactly industrial-strength, and leans towards simplicity over performance. Still, it can decompose 100k-vertex triangulations in a few seconds. I'm open to feature requests.
Congratulations to my (now former) student, Luís Fernando Schulz Xavier da Silveira, who successfully defended his PhD thesis titled Turán Triangles, Cell Covers, Road Placement and Train Scheduling on Monday.
This is the first thesis defense I've taken part in where no two participants were in the same room.
A few weeks ago, I posted a photo of some happy people who had just proven a theorem a few minutes earlier.
That theorem appears in the arXiv today and the theorem is the title of the paper: Planar Graphs Have Bounded Queue Number.
More important than theorem though, is the tool used to prove it: layered $H$-partitions of small layered width where $H$ has small treewidth.
Expect another result tomorrow: Planar Graphs Have Bounded Nonrepetitive Chromatic Number.
Professor of Computer Science at Carleton University
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