notes

• Local Langlands parameters (Academia Sinica, 2023)
  Basic background material on local Langlands parameters and their moduli stacks.


• Categorical centers and traces (Academia Sinica, 2022)
  Discusses generalities on traces in classical, then categorical, then 2-categorical settings, and their iterated nature. Discussion of the example of convolution categories, then an application to categorical local Langlands.


• What is an ind-coherent sheaf? (UC Berkeley, 2017)
  An introduction to the notion of ind-coherent sheaves. Starts from classical relaizations, then moves to Gaitsgory's definition, with some examples.


• Beilinson-Bernstein over the base affine (UC Berkeley, 2015)
  An overview of a paper by Ben-Zvi and Nadler introducing a Beilinson-Bernstein "in families" over the central character. Introduces equivariant D-modules, Barr-Beck formalism, and computes some examples.


• Local Systems and Derived Algebraic Geometry (UC Berkeley, 2015)
  An introduction to the derived moduli stack of local systems on a topological space. Background on stacks and some motivation for considering derived stacks.


• Equivariant Cohomology and Koszul Duality (UC Berkeley, 2013)
  An introduction to the notions of equivariant cohomology, and its Koszul dual ("de-equivariantized") presentation in homology. A discussion and some motivation for studying differential graded rings (rather than cohomology rings). The localization theorem.