Peter Woit

We describe the relation between vectors and spinors in complex spacetime in an unconventional chirally asymmetric manner, using purely right-handed spinors, with Minkowski spacetime getting Wick rotated to a four-dimensional Euclidean…

For many years now it has become conventional for theorists to argue that "space-time is doomed", with the difficulties in finding a quantum theory of gravity implying the necessity of basing a fundamental theory on something quite…

Remarkably, the twistor $\mathbf P^1$ occurs as a fundamental object in both four-dimensional space-time geometry and in number theory. In Euclidean signature twistor theory it is how one describes space-time points. In recent work by…

Taking Euclidean signature space-time with its local Spin(4)=SU(2)xSU(2) group of space-time symmetries as fundamental, one can consistently gauge one SU(2) factor to get a chiral spin connection formulation of general relativity, the other…

Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…

A polemical article evaluating string theory from the point of view of a quantum field theorist working in a mathematics department. Comments to the author are encouraged.

A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.