Gil Kalai writes the “Combinatorics and more” blog. I find many of his posts on the blog to be detailed and nicely structured. Here are just a few of the recent ones I enjoyed.

“Possible future Polymath projects (2009, 2021)”

I always think it’s interesting to explore which big research questions attract a lot of interest. For those who aren’t familiar with polymath projects, this post describes what they are and gives updates on potential polymath projects that Tim Gowers suggested on his blog in 2009. Kalai also suggests some possible future directions for polymath projects and asks “meta questions,” such as “What is the ideal platform for a polymath project?” and, my personal favorite, “Are polymath projects inviting in terms of diversity of participants?”

The “To cheer you up in difficult times” posts

So far, Kalai has created 19 “To cheer you up in difficult times” posts, including this one about a proof of the Erdős-Faber-Lovász conjecture uploaded to arXiv by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus and

“To cheer you up in difficult times 13: Triangulating real projective spaces with subexponentially many vertices” about another new paper posted to arXiv by Karim Adiprasito, Sergey Avvakumov, and Roman Karasev.

This post is replete with interesting bits of information about recent papers, videos from some of Kalai’s lectures and even “a small taste of quantum poetry for the skeptics.”

Besides all of the interesting posts by Kalai, there are also a bunch of guest posts worth checking out. Here are just a few:

“Dan Romik on the Riemann zeta function”

“Recently when I was thinking about the Riemann zeta function, I had the double thrill of discovering some new results about it, and then later finding out that my new ideas were closely related to some very classical ideas due to two icons of twentieth-century mathematics, George Pólya and Pál Turán,” Romik wrote in the beginning of the piece.

In this post, Bárány explains limit shapes and the limit shape theorem, limit shapes for polygons in convex bodies and more.

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