Manifolds with generalized corners (g-corners), introduced by Joyce, are spaces that locally look like rational polyhedral cones. We describe the notion of b-complex manifolds with g-corners and establish an analogue of the (formal) Newlander–Nirenberg theorem ensuring the existence of local complex coordinates on such manifolds. We also show that Kato–Nakayama spaces associated to log smooth complex analytic…

We study boomerangs in the derived category of an elliptic curve C. These are filtrations of the zero object whose factors are polystable objects with strictly increasing phase. The numerical invariants of a boomerang are given by the Chern characters of the direct summands of these factors, which together determine a lattice polygon. When this polygon is a T-polygon,…

Ring extensions and complexification are classical constructions in algebra and number theory, inducing adjunctions between module categories. Interestingly, closely related number-theoretic structures also play a central role in modern quantum circuit synthesis. I will explain how these ideas meet in the technique of catalytic embedding, and describe a categorical framework that naturally generalises this construction. (Work in progress with Andrew Glaudell, Julien Ross, Matt Amy, Robin Kaarsgaard, and Sam Mendelson.)

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