Ben Williams | PIMS - Pacific Institute for the Mathematical Sciences

Toric topology assigns to each simplicial complex K a space with a torus action, called the moment-angle complex, which is defined as a polyhedral product or (homotopy) colimit over the face category of K. These spaces play a universal role in toric...

Given two manifolds M and N, one can ask whether it is possible to cut M up into pieces and reassemble them to obtain N. This “cut-and-paste” (SK) relation fits into the framework of scissors congruence K-theory, which is an extension of higher...

There is a striking and useful analogy between equivariant homotopy theory and functor calculus. In the equivariant setting, Greenlees conjectured that the category of rational G-spectra has an algebraic model - meaning it is equivalent to the...

This is joint work with Uriya First. If $R$ is a ring and $n$ is a natural number, then an Azumaya algebra of degree $n$ on $R$ is an $R$-algebra such that $A$ becomes isomorphic to the $n \times n$ matrix algebra after some faithfully flat extension...

An Azumaya algebra is something that is "locally" isomorphic to a matrix algebra. By varying the sense of "locally", we arrive at different incarnations of the concept. The motivating example is that of central simple algebras over a field. In this...

In an Exposé published in 1968, Alexander Grothendieck generalized the notion of a central simple algebra over a field by defining Azumaya algebras in locally ringed topoi. Specific examples of Azumaya algebras in locally ringed topoi include (up to...

If X is a variety over a field, the Chow groups of X are defined in terms of closed subvarieties of X and form a kind of cohomology theory for X. Higher Chow groups, defined by Spencer Bloch in the 1980s in terms of subvarieties on X x A^m and now...

The classical EHP sequence is a partial answer to the question of how far the unit map of the loop-suspension adjunction fails to be a weak equivalence. It can be used to move information from stable to unstable homotopy theory. I will explain why...

The algebraic K-theory, due to Quillen, of a field is related to a theory defined by Milnor called Milnor K-theory and denoted K^M. In the 1980s, Andrei Suslin constructed a map K_n(F) -> K^M_n(F), and conjectured that the image was the subgroup (n-1...