Activities This Week
BGU Probability and Ergodic Theory (PET) seminar
Non-trivial phase transition in percolation
Nov 19, 11:10—12:00, 2020, Online
Speaker
Ariel Yadin (Ben-Gurion University)
Abstract
In 1920 Ising showed that the infinite line Z does not admit a phase transition for percolation. In fact, no “one-dimensional” graph does. However, it has been asked if this is the only obstruction. Specifically, Benjamini & Schramm conjectured in 1996 that any graph with isoperimetric dimension greater than 1 will have a non-trivial phase transition.
We prove this conjecture for all dimensions greater than 4. When the graph is transitive this solves the question completely, since low-dimensional transitive graphs are quasi-isometric to Cayley graphs, which we can classify thanks to Gromov’s theorem.
This is joint work with H. Duminil-Copin, S. Goswami, A. Raufi, F. Severo.
Arithmetic applications of o-minimality
On the Diophantine applications of the Pila Wilkie theorems Online
Nov 24, 10:10—12:00, 2020, online
Speaker
Kobi Peterzil (Haifa)
Jerusalem - Be'er Sheva Algebraic Geometry Seminar
Bad reduction and fundamental groups
Nov 25, 15:00—16:30, 2020,
Speaker
Netan Dogra (Oxford)
Abstract
This talk will be about two related results concerning Galois actions on pro-p fundamental groups of curves over mixed characteristic local fields, with applications to the algorithmic resolution of Diophantine equations. The first result is joint with Alex Betts, and gives a description of how the Galois action on the fundamental group varies with the choice of basepoint in terms of harmonic analysis on the dual graph of the special fibre of a stable model (when p is different from the residue characteristic). The second result is joint with Jan Vonk, and gives a description of how to compute the Galois action (in a p-adic Hodge theoretic sense) when the residue characteristic is p and the curve has semistable reduction.