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math.AG2026
Affine Springer fiber and the small quantum group
Roman Bezrukavnikov, Pablo Boixeda Alvarez, Michael McBreen +1
We find a new geometric incarnation for the principal block in the category of modules over a quantum group at a root of unity, realizing it as a full subcategory of microsheaves o…
math.AG2025
Homological Mirror Symmetry for Hypertoric Varieties I
Michael McBreen, Ben Webster
We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertori…
math.AG2024
Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
Benjamin Gammage, Michael McBreen, Ben Webster
In this paper, we prove a homological mirror symmetry equivalence for pairs of multiplicative hypertoric varieties, and we calculate monodromy autoequivalences of these categories…