# Tag Info

### Convex polygon shadows: Shortest equivalent segments

The current best lower bound on the total length of segments in $S$ is 2.00002: A. Kawamura, S. Moriyama, Y. Otachi and J. Pach, A lower bound on opaque sets, Comput. Geom. 80 (2019), 13–22. https://...
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1 vote

### Question on consecutive integers with similar prime factorizations

This is how Heath-Brown resolved the d(n)=d(n+1) problem ! The idea is due to Claudia Spiro who used it for d(n)=d(n+5040) but was unable to reduce the 5040. The same idea has now been used in many ...
1 vote

### Birkhoff conjecture about integrable billiards

I think has recently obtained partial results on this conjecture (On polynomially integrable Birkhoff billiards on surfaces of constant curvature, JEMS 2021)
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### Mark Hovey's open problems in the theory of model categories

On the other hand, the category of commutative monoids seems to be much more subtle. The conditions for the existence of a model structure on commutative monoids were worked out by Jacob Lurie around ...
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