Here are a couple of problems that I am interested in and are not well-known.

**Problem 1 ($100):** Prove that . See this paper of mine for definitions and context. As a warm up, one may wish to prove for $25.

**Problem 2 ($50):** Prove that , where is finite and is rotation by 90 degrees. For a warm–up, $25 for a proof or disproof that . See this paper of mine or problem 5 of Boris Bukh’s website. **Update: **The warm-up was recently solved by Akshat Mudgal in the affirmative.

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