פעילויות בתאריכים מאי 20-26, 2018
גיאומטריה ותורת החבורות
מאי 20, 14:30-15:30, 2018, -101
Maria Hempel (HUJI)
מאי 21, 14:10-15:10, 2018, -101
Yotam Svoray (BGU)
We present a two-player combinatorial game over a $k$-ary shift-register and analyze it. The game is defined such that, for each of the player, the only way to avoid losing is to play such that the next state of the game is the next window in the well known prefer-max De Bruijn sequence. We then proceed to solve the game, i.e., to propose efficient algorithms that compute the moves for each player. Finally, we show how these algorithms can be combined into an efficiently computable shift-rule for the prefer-max sequence.
BGU Probability and Ergodic Theory (PET) seminar
מאי 22, 11:00-12:00, 2018, 201
Idan Perl (BGU)
Spaces of harmonic functions on a given group have a strong relationship with its large-scale geometry. Classically, mostly bounded harmonic functions have been studied. We review some results about bounded harmonic functions and present the recent research on spaces of unbounded harmonic functions.
מאי 22, 14:30-15:30, 2018, Math -101
Uriya First (University of Haifa)
The primitive element theorem states that every finite separable field extension is generated by a single element. Another classical result states that every central simple algebra is generated by 2 elements over its center. When the base field is replaced with a (commutative) ring, separable extensions and central simple algebras have natural generalizations called finite etale algebras and Azumaya algebras, respectively. After recalling their definition, I will discuss a joint work with Zinovy Reichstein where we generalize the previous results to such algebras. Specifically, we show that when the base ring is noetherian of Krull dimension d and has no finite epimorphic images, every finite etale algebra is generated by d+1 elements and every Azumaya algebra is generated by d+2 elements. In fact, our result applies to a wider range of algebras, and includes as special cases results of Forster and Swan on the number of generators of finitely generated projective modules over a ring of Krull dimension d.
I will also discuss the question of whether our bounds are optimal and several applications to constructing “highly generic” principal homogeneous bundles.
מאי 22, 16:15-18:00, 2018, -101
מאי 22, 18:00-19:30, 2018, אולם 101-
באופן שאולי נראה קצת מפתיע למתבונן מבחוץ, התורה של פעולות של חבורות על עצים משחקת תפקיד מפתח בתורת החבורות ובגיאומטריה. אנסה להציג טעימה מן התורה הזו.