activities on Apr 22-28, 2018
BGU Probability and Ergodic Theory (PET) seminar
A power-law upper bound on the decay of correlations in the two-dimensional random-field Ising model
Apr 24, 11:00-12:00, 2018, 201
Ron Peled (Tel Aviv University)
The random-field Ising model (RFIM) is a standard model for a disordered magnetic system, obtained by placing the standard ferromagnetic Ising model in a random external magnetic field. Imry-Ma (1975) predicted, and Aizenman-Wehr (1989) proved, that the two-dimensional RFIM has a unique Gibbs state at any positive intensity of the random field and at all temperatures. Thus, the addition of an arbitrarily weak random field suffices to destroy the famed phase transition of the two-dimensional Ising model. We study quantitative features of this phenomenon, bounding the decay rate of the effect of boundary conditions on the magnetization in finite systems. This is known to decay exponentially fast for a strong random field. The main new result is a power-law upper bound which is valid at all field strengths and at all temperatures, including zero. Our analysis proceeds through a streamlined and quantified version of the Aizenman-Wehr proof. Several open problems will be mentioned. Joint work with Michael Aizenman.
Apr 24, 14:30-15:30, 2018, Math -101
Nir Lazarovich (Technion)
Accessibility is an important concept in the study of groups and manifolds as it helps decomposing the object in question into simpler pieces. In my talk I will survey some accessibility results of groups and manifolds, and explain how to relate the two. I will then discuss a joint work with Benjamin Beeker on a higher dimensional version of these ideas using CAT(0) cube complexes.
Apr 24, 16:15-18:00, 2018, -101
Algebraic Geometry and Number Theory
Apr 25, 15:10-16:30, 2018, Math -101
Ambrus Pál (Imperial College London)
We prove that for a smooth, projective, geometrically irreducible variety X equipped with a dominant morphism f with a smooth generic fibre onto a smooth projective rational variety over the function field R(C) of a smooth, irreducible projective curve C over the reals R such that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global principle for rational points for the smooth fibres of f over R(C)-valued points, then the same holds for X, too, by adopting the fibration method similarly to Harpaz–Wittenberg. We also show that the strong vanishing conjecture for n-fold Massey products holds for fields of virtual cohomological dimension at most 1 using a theorem of Haran. Joint work with Endre Szabó.