Topological phases of matter exhibit Bott-like periodicity with respect to

time-reversal, charge conjugation, and spatial dimension. I will explain how

the non-commutative topology in topological phases originates very generally

from symmetry data, and how operator K-theory provides a powerful and

natural framework for studying them.

# Past Quantum Field Theory Seminar

We will discuss the relation between perturbative gauge theory and

perturbative gravity, and look at how this relation extends to some exact

classical solutions. First, we will review the double copy prescription that

takes gauge theory amplitudes into gravity amplitudes, which has been

crucial to progress in perturbative studies of supergravity. Then, we will

see how the relation between the two theories can be made manifest when we

restrict to the self-dual sector, in four dimensions. A key role is played

by a kinematic algebraic structure mirroring the colour structure, which can

be extended from the self-dual sector to the full theory, in any number of

dimensions. Finally, we will see how these ideas can be applied also to some

exact classical solutions, namely black holes and plane waves. This leads to

a relation of the type Schwarzschild as (Coulomb charge)^2.