# Fortnightly links (141)

Noah Olander: Fully faithful functors and dimension is a (very short) preprint that settles an interesting open problem. Namely if $\mathbf{D}^{\mathrm{b}}(X)$ is an admissible subcategory of $\mathbf{D}^{\mathrm{b}}(Y)$, do we have $\dim X\leq\dim Y$? The case of an equivalence was known (by the properties of the Serre functor), but the general case was something that every so often would come up in conversation and no-one would have an idea. Now we know!

Jonny Evans: Lagrangian torus fibrations is a really nice set of notes, for anyone like me who's always trying to learn more symplectic geometry.

Bradley Doyle: Homological projective duality for the Plücker embedding of the Grassmannian is a PhD thesis that establishes homological projective duality (in an abstract sense) for Grassmannians, by studying noncommutative resolutions of affine cones over Grassmannians. Cool! It was this thesis that lead to my previous blogpost by the way.