Adeel A. Khan

I’m a mathematician currently based at IHES as a post-doc in the Simons Collaboration on Homological Mirror Symmetry.

I mostly study cohomological invariants in algebraic and differential geometry, especially of spaces with singularities. If you’re interested, you can find a selection of some of my work below. Alternatively, here’s a full list of my papers and lecture notes.

My e-mail address is [email protected]

Non-transversality in algebraic geometry

A typical way singularities arise is in case of non-transverse intersections of smooth ambient spaces. Derived algebraic geometry affords a powerful way to study such situations via the notion of quasi-smoothness. Here are a few papers illustrating this idea.

Structure of the motivic homotopy category

Voevodsky’s stable motivic homotopy category is designed to give a sheaf-theoretic approach to cohomology theories like the (higher) Chow groups, algebraic cobordism, and algebraic K-theory. The papers below prove some structural results about this category.

Elsewhere

Here are some more resources related to the above topics that are available elsewhere on the web.