Activities This Week
AGNT
Prime torsion in the Tate-Shafarevich groups of abelian varieties over $\mathbb{Q}$
Nov 3, 16:00—17:15, 2021, -101
Speaker
Ariel Weiss (BGU)
Abstract
Very little is known about the Tate-Shafarevich groups of abelian varieties. On the one hand, the BSD conjecture predicts that they are finite. On the other hand, heuristics suggest that, for each prime $p$, a positive proportion of elliptic curves $E/\mathbb{Q}$ have $\Sha(E)[p] \ne 0$, and one expects something similar for higher dimensional abelian varieties as well. Yet, despite these expectations, it seems to be an open question whether, for each prime $p$, there exists even a single elliptic curve over $\mathbb{Q}$ with $\Sha(E)[p] \ne 0$. In this talk, I will show that, for each prime $p$, there exists a geometrically simple abelian variety $A/\mathbb{Q}$ with $\Sha(A)[p]\ne 0$. Our examples arise from modular forms with Eisenstein congruences. This is joint work with Ari Shnidman.
BGU Probability and Ergodic Theory (PET) seminar
Bohr Chaos and Invariant Measures Online
Nov 4, 11:10—12:00, 2021, Building 34, room 14
Speaker
Matan Tal (The Hebrew University)
Abstract
A topological dynamical system is said to be Bohr chaotic if for any bounded sequence it possesses a continuous function that correlates with the sequence when evaluated along some orbit. The theme of the lecture will be the relation of this property to an abundance of invariant measures of the system.
Colloquium
Order and disorder in multiscale substitution tilings
Nov 9, 14:30—15:30, 2021, Math -101
Speaker
Yotam Smilansky (Rutgers University)
Abstract
The study of aperiodic order and mathematical models of quasicrystals is concerned with ways in which disordered structures can nevertheless manifest aspects of order. In the talk I will describe examples such as the aperiodic Penrose and pinwheel tilings, together with several geometric, functional, dynamical and spectral properties that enable us to measure how far such constructions are from demonstrating lattice-like behavior. A particular focus will be given to new results on multiscale substitution tilings, a class of tilings that was recently introduced jointly with Yaar Solomon.
אשנב למתמטיקה
כאשר (כמעט) כל האיברים של חבורה נראים אותו הדבר Online
Nov 9, 18:10—19:30, 2021, בניין 32 חדר 309 וכן במרשתת
Speaker
יאיר גלזנר
Abstract
בחבורות טופולוגיות רבות מתגלה תופעה מפתיעה: יש מחלקת צמידות אחת הרבה יותר גדולה מכל השאר (למשל במובן משפט הקטגוריה של בייר). נראה שלתופעה זו יש מסקנות אלגבריות חזקות ומפתיעות.