You can find the expository work I've written through the years, and in addition to the listings, I have included short summaries of their content.
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 technique 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; the globalization part is a joint work with Laurent Côté, David Nadler, and Vivek Shende in Perverse Microsheaves and The microlocal Riemann-Hilbert correspondence for complex 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, taken from an earlier version of the work by Nadler and Shende, Sheaf quantization in Weinstein symplectic manifolds, v2, and how sheaf theory can be applied to solve symplectic geometric questions. Lastly, we reverse the direction to show how symplectic results can be used to solve questions in sheaf theory as well.
Mostly expository notes summarizing the basic toolkit in microlocal sheaf theory, such as microsheaves, which provides new categories that addmit a microlocalization map from the category of sheaves, and isotopies of sheaves, which allows one to deform sheaves as if they are Lagrangian submanifolds. This last trick proivdes a geometric description of the Serre functor on certain categories of constructible sheaves, as described in my joint work with Li, Spherical adjunction and Serre functor from microlocalization.
Expository notes on the second half of my thesis, which is now included in my joint work with Wenyuan Li, Spherical adjunction and Serre functor from microlocalization and Duality, Künneth formulae, and integral transforms in microlocal geometry. 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. In addition, we include a few well-known guiding examples from derived algebraic geometry, which inspired our work. The talk was recorded by the hosting institute.
Expository notes on the first half of my thesis Wrapped sheaves 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 (and the notes thus contains many pictures.)
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 Rodríguez Camargo's detailed notes on solid geometry, which can be found on his website.
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. In short, there is a functorial identification on derived schemes between the free loop space and the tangent cotangent bundle, which recovers the classical HKR equivalence after taking global sections.
Graduate student expository notes covering the Koszul dual of an algebra and its construction through generators and relations.