You can find the expository work I've written through the years; in addition to the listings, I have included short summaries of their content on this page.
This part collects expository notes and summaries of my own research papers, written with a general geometry audience in mind:
A more technical version of the expository notes, Riemann-Hilbert on contact manifolds below. We mostly restrict ourselves to the constructible sheaf side and focus on the technical notion of microstalks. Here, we recall the classical construction by Kashiwara and Schapira and compare it with the new construction built upon the general machinery from Sheaf quantization in Weinstein symplectic manifolds, which we summarize in the notes, and use it to give a global definition of microlocal perverse t-structure.
Mostly expository notes summarizing the Riemann-Hilbert correspondence and their upgrades through microlocalization and gluing over contact manifolds. As the notes are expository, we use the simplest cases over the affine line to test various notions, including the solution functor and the notion of microlocalization on the two sides. Some slides can be found here as well.
A general discussion aimed at topologists. The notes begin by discussing why symplectic geometry often recovers differential topology through the "phase space." Then, we explain the relation between Lagrangians and sheaves from this viewpoint and how sheaf theory can be applied to solve symplectic geometric questions.
Mostly expository notes summarizing the basic toolkit in microlocal sheaf theory, such as microsheaves and isotopies of sheaves. This last trick provides a geometric description of the Serre functor on certain categories of constructible sheaves.
Expository notes on the second half of my thesis. The main point of the notes is to explain the general paradigm of non-commutative geometry and how it is realized in the case of constructible sheaves via isotopies of sheaves. The talk was recorded by the hosting institute.
Expository notes on the first half of my thesis where we systematically develop applications of the notion of isotopies of sheaves. Compared to the paper, we include fewer categorical details and focus more on the geometry.
Expository notes on key papers and results by other authors:
Expository notes explaining how analytic stacks are constructed from analytic rings and the D-topology coming from six-functor formalism. One can view these notes as a quick summary of RodrÃguez Camargo's detailed notes on solid geometry.
Graduate student expository notes explaining Auroux's survey papers on the SYZ construction.
Graduate student expository notes explaining one of the main results in Loop spaces and connections by Nadler and Ben-Zvi.
Graduate student expository notes covering the Koszul dual of an algebra and its construction through generators and relations.