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Regeneration of Elliptic Chains with Exceptional Linear Series
(2014-06-06)
We study two dimension estimates regarding linear series on algebraic curves. First, we generalize the classical Brill-Noether theorem to many cases where the Brill-Noether number is negative. Second, we extend results of ...
Categorical Moy-Prasad theory and applications to geometric Langlands
(2022-05-10)
For any $G((t))$-category, we define a filtration which provides a categorification of the notion of depth studied by Moy and Prasad in the context of representations of a p-adic group. We also prove a generation statement ...
A Functorial Perspective on Homological Mirror Symmetry for Hypersurfaces
(2023-06-01)
In this thesis, we prove two homological mirror symmetry results for hypersurfaces of different kinds. In the first, we consider a definition of the Fukaya category of a singular hypersurface proposed by Auroux, given by ...
On the nef and effective cones of Hilbert schemes of points in projective space
(2023-05-16)
We compute the nef cones in codimensions 2 & 3 and the effective cones in dimensions 2 & 3 for the Hilbert scheme of three points in $\mathbb{P}^3$. This involves studying the orbits of the PGL action on the Hilbert scheme, ...