# Forthcoming & Recent Colloquia

To be announced.

## Recent Events

#### Quantum Field Theory and Random Walk.

Wednesday 15 February 2017 at 3pm, Pevensey-1 1A6.  Refreshments afterwards in Pevensey-2 foyer.

Professor David Brydges, Professor Emeritus of Mathematics at the University of British Colombia.

Abstract:  Quantum field theories are defined by axioms, but for this introduction I discuss a single example called Euclidean φ4 and put the emphasis on connections with familiar topics in mathematics, especially random walk. I will review (1) why φ4 is simultaneously a theory of fields and a theory of particles that are created and annihilated, (2) a famous negative result for existence in more than four dimensions, (3) the relation of φ4 to self-avoiding walk.

#### Introduction to the Renormalisation Group

Thursday 16 February 2017 at 3pm, Pevensey-3, 5C11.

Professor David Brydges, Professor Emeritus of Mathematics at the University of British Colombia.

Abstract:  The $\varphi^{4}$ model on the lattice $Z^{d}$ is a variation on the Ising model: instead of requiring, for every lattice site $x$, that the spin $\varphi_{x}$ is exactly plus or minus one, $\varphi_{x}$ is real valued, but concentrated near $\pm 1$. With Roland Bauerschmidt and Gordon Slade I have recently used a rigorous version of the Wilson renormalisation group to prove that, on the four dimensional lattice, critical exponents of the $\varphi^{4}$ model and related models such as self-avoiding walk have the precise logarithmic corrections predicted by theoretical physics. I will explain some of the ideas.