## Kirill Polovnikov (LPTMS (visitor), Skoltech & Laboratoire Poncelet)

### Constrained fractal polymer chain in curved geometry: how far is KPZ?

Can intrinsic curvature of the space yield a similar regime of fluctuations as a certain type of random potentials? In this talk by means of scaling analyses of the free energy and computer simulations I will discuss stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. The typical excursions of the polymer away from the surface scale as \Delta \sim R^{\beta}, with the Kardar-Parisi-Zhang (KPZ) growth exponent \beta=1/3 and the curvature-induced correlation length is described by the KPZ exponent z=3/2. Remarkably, the uncovered KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across the classical polymer models, e.g. SAW, randomly-branching polymers, crumpled unknotted rings. The one-point distribution of fluctuations, as found in simulations, can be well described by the squared Airy law, connecting our 2D polymer problem with the (1+1)D Ferrari-Spohn universality class of constrained random walks. A relation between directed polymers in quenched random potential (KPZ) and stretched polymers above the semicircle will be explained.