Activities This Week
Arithmetic applications of o-minimality
אשנב למתמטיקה
אנליזה פוגשת אריתמטיקה Online
Jun 8, 16:10—17:30, 2021, מרשתת
Speaker
נדיה גורביץ'
Abstract
מכונת מזל מדפיסה שני מספרים שלמים אקראים. אם הם זרים - הנכם מקבלים 10 שקלים. מחיר המשחק הוא 6 ש”ח. האם כדאי לכם להשתתף?
נראה איך ניתן לנחש את התשובה בקלות ואז נוכיח אותה תוך כדי שימוש בפונקציות אריתמטיות
Jerusalem - Be'er Sheva Algebraic Geometry Seminar
TBA
Jun 9, 15:00—16:30, 2021,
Speaker
Uri Brezner (HUJI)
BGU Probability and Ergodic Theory (PET) seminar
Linear repetitivity in polytopal cut and project sets Online
Jun 10, 11:10—12:00, 2021, Online
Speaker
Henna Koivusalo (University of Bristol)
Abstract
Cut and project sets are aperiodic point patterns obtained by projecting an irrational slice of the integer lattice to a subspace. One way of classifying aperiodic sets is to study the number and repetition of finite patterns. Sets with patterns repeating linearly often, called linearly repetitive sets, can be viewed as the most ordered aperiodic sets. Repetitivity of a cut and project set depends on the slope and shape of the irrational slice. In an earlier work, joint with of Haynes and Walton, we showed that when the slice has a cube shape, linear repetitivity holds if and only if the following two conditions are satisfied: (i) the cut and project set has the minimal number of different finite patterns (minimal complexity), and (ii) the irrational slope satisfies a badly approximable condition. In a new joint work with Jamie Walton, we give a generalisation of this result to all convex polytopal shapes satisfying a mild geometric condition. A key step in the proof is a decomposition of the cut and project scheme, which allows us to make sense of condition (ii) for general polytopal windows.