Francis Bischoff

In this blog post, I want to explain a way in which I like to motivate Lie groupoids via the theorem on the existence and uniqueness of solutions to ordinary differential equations.

The Stasheff Associahedra are a family of polytopes that seem to be ubiquitous, but in particular are strongly linked to associativity.

What is the volume of a ball of dimension and radius ?

In my last post, I told you how to encode the zero locus of a polynomial function in terms of an -algebra structure on , where lies in degree and lies in degree .

A fundamental principle of derived deformation theory is that a formal “space” (i.e. formal moduli problem) can be encoded by a differential graded Lie algebra, or more generally, an -algebra.

The character varieties are a remarkable family of spaces that lie at the center of many different active strands of research of the past 30 or 40 years.

Let be a holomorphic line bundle over a complex manifold .

An absolutely central concept/tool in modern mathematics is that of (co)homology.

In this post I will discuss a construction, due to Deligne, for extending a flat vector bundle to a flat logarithmic vector bundle.

Consider the exponential map for matrices , which can be defined by the formula where is a square matrix.