Activities This Week

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.

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.

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.

We shall show that the automorphism group of octonion algebra is isomorphism to the simple group of type G2