09:00 to 10:00 Roland Bauerschmidt (University of Cambridge)Spectral gap critical exponent for Glauber dynamics of hierarchical spin models We develop a renormalisation group approach to deriving the asymptotics of the spectral gap of the generator of Glauber type dynamics of spin systems at and near a critical point. In our approach, we derive a spectral gap inequality, or more generally a Brascamp--Lieb inequality, for the measure recursively in terms of spectral gap or Brascamp--Lieb inequalities for a sequence of renormalised measures. We apply our method to hierarchical versions of the $4$-dimensional $n$-component $|\varphi|^4$ model at the critical point and its approach from the high temperature side, and the $2$-dimensional Sine--Gordon and the Discrete Gaussian models in the rough phase (Kosterlitz--Thouless phase). For these models, we show that the spectral gap decays polynomially like the spectral gap of the dynamics of a free field (with a logarithmic correction for the $|\varphi|^4$ model), the scaling limit of these models in equilibrium. Co-author: Thierry Bodineau INI 1 10:00 to 11:00 Gordon Slade (University of British Columbia)Renormalisation group and critical phenomena - 4 The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt. INI 1 11:00 to 11:30 Morning Coffee 11:30 to 12:30 Gordon Slade (University of British Columbia)Renormalisation group and critical phenomena - 3 The understanding of critical phenomena via the renormalisation group approach is one of the great achievements of theoretical physics during the last half of the previous century. This series of lectures will begin with an introduction to the critical behaviour of the phi^4 lattice spin system and its supersymmetric counterpart (the weakly self-avoiding walk). The lectures will mainly be occupied with an introduction to a rigorous renormalisation group method that has been developed and used to compute critical exponents for these models in the upper critical dimension d=4, and also below the critical dimension for long-range models. The lectures are based on collaborations with David Brydges and Roland Bauerschmidt. INI 1 12:30 to 13:30 Buffet Lunch at INI 13:30 to 14:30 Massimiliano Gubinelli (Universität Bonn)A stochastic approach to constructive QFT Co-author: Nikolay Barashkov (University of Bonn)We propose a new existence proof of the Phi^4_{2,3} Euclidean quantum fields in a periodic domain using tools from stochastic analysis, in particular a stochastic control interpretation of Wilson's continuous RG. INI 1