Abstract: Joint work with C. Garban. KT or topological phase transitions are a type of phase transition discovered by Kosterlitz and Thouless in the ’70s. Models that undergo this phenomenon are typically 2-dimensional and do not have a classical phase transition. In this talk, I will explain this type of phase transition going over the first proof of their existence by Fröhlich and Spencer which relates them to the localisation of random surfaces. Then, I will discuss a new interpretation of this phase transition that arises from the following question: Let $\phi$ be a discrete Gaussian free field at temperature $T$ and imagine that you lost its integer part, can you recover the macroscopic information of $\phi$?.
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