# George Johnson

# George Johnson

Graduate Student

I'm a third year DPhil student in the Particle Theory group, supervised by John March-Russell. I did my undergraduate studies (BA Natural Sciences, MMath) at Cambridge.

Currently I'm interested in several topics within high energy theory:

**Quantum Aspects of Black Holes**

I'm presently working on topics related to Hawking radiation.

**Solitons**

Solitons are non-trivial solutions to classical field equations which are localised in space. They are stable with respect to decay into lower energy field configurations (such as a uniform field) by virtue of some conserved charge, which may be topological in nature, or which may arise as a result of a continuous global symmetry. Topological solitons are an interesting application of ideas in homotopy theory, with the topological charge of many solitons being given by the homotopy class of a map from an n-dimensional sphere 'at infinity' in real space to some manifold in field space. Non-topological solitons, such as Q-balls, are the lowest energy field configurations of a given *Noether* charge, such as particle number. They can be thought of as aggregates of the fundamental particles in the theory, and are stabilised by some attractive interaction between them.

**The Weak Gravity Conjecture**

In our universe it is observed that gravity is (by far) the weakest of the four fundamental forces. The weak gravity conjecture asserts that this is no coincidence, and that in fact gravity will be the weakest force in any consistent quantum theory of gravity. The arguments are based upon ideas surrounding the need for extremal black holes (those with a mass equal to their charge, in appropriate units) to be able to decay. This is in turn connected to the black hole information paradox. If the weak gravity conjecture is true, it provides a powerful sieve for rejecting low energy effective theories developed for the purposes of phenomenology, which typically ignore gravity entirely, and often involve new forces which interact extremely weakly with the particles we know of.

Finally, I have a passion for all things mathematical. Here are some things you might not know:

- A symmetric random walk on a square lattice in one or two dimensions will visit, with unit probability, every lattice site. In higher dimensions this is not true.
- The n-dimensional unit sphere with the largest 'surface area' is the 7-sphere.
- The smallest non-Abelian group of odd order has 21 elements (and is unique).