%0 Conference Paper %F Oral %T Introduction to the Renormalization group. %+ Laboratoire Charles Coulomb (L2C) %A Mitter, Pronob %F Invité %< sans comité de lecture %Z L2C:18-198 %B Scaling limits, rough paths, quantum field theory %C Cambridge, United Kingdom %8 2018-09-03 %D 2018 %K Renormalization group %K rigorous control for a non-gaussian fixed point %K multi-scale expansions %K Gaussian fixed points %K discrete flows %K continuous flows %K ultraviolet cutoff removal %K critical field theories %Z Physics [physics]/Mathematical Physics [math-ph] %Z Mathematics [math]/Mathematical Physics [math-ph]Conference papers %X In these lectures I will introduce and explore properties of the Renormalisation Group (RG) both in its discrete and continuous forms. Topics to be discussed include multi scale expansions, the RG, Gaussian fixed points, Wick products from the RG point of view, ultraviolet cutoff removal, flow equations and perturbative flows, trivial and non-trivial fixed points, and critical field theories. Rigorous Discrete RG analysis. I will discuss a rigorous application for a non-trivial fixed point. %G English %L hal-01935444 %U https://hal.science/hal-01935444 %~ CNRS %~ L2C %~ TDS-MACS %~ MIPS %~ UNIV-MONTPELLIER %~ UM-2015-2021