... Only innocence can surmount them, which mere knowledge doesn't even take into account, in those moments when we find ourselves able to listen to things, totally and intensely absorbed in child's play. — Alexander Grothendieck « Récoltes et Semailles »
Maximally Frobenius-destabilized vector bundles over smooth algebraic curves (2014). arXiv:1408.5117.
Essentially, when a vector bundle becomes very, very unstable after Frobenius pullback, we can learn a lot about the stability of the bundle itself (depending on whether its rank is larger than, equal to, or lower than the characteristic p).
Limiting behavior of Donaldson's heat flow on non-Kähler surfaces (2013-2014, with Jacob McNamara). arXiv:1403.8037.
Lifting representations of finite reductive groups: a character relation (2011-2012, with Jeffrey Adler et al). arXiv:1205.6448.
Seminar: ind-coherent sheaves
Justin Campbell, Hunter Spink, and I are organizing a seminar on derived algebraic geometry, with an emphasis on the theory of ind-coherent sheaves. Here is the seminar page.
Old learning notes
(Warning: I make mistakes! If you find them, email me.)
The Bondal-Orlov reconstruction theorem. pdf.
These are notes for my talk at AGLS.
Deligne's theorems on degeneration of spectral sequences. pdf.
Leray spectral sequence and Hodge-de Rham spectral sequence.
Finite and abelian affine group schemes. pdf.
Cartier duality, étale group schemes, group schemes of multiplicative type.
Tensor product of semistable vector bundles over curves in characteristic zero. pdf.
Namely, the tensor product is still semistable. Almost all technical ingredients are explained in detail.
Other things that you may find interesting
The Stacks Project. Link.