Activities This Week

בהרצאה נדבר על הצגות של חבורות (ולא רק חבורות). תורת ההצגות היא המשך טבעי למושג ”פעולה של חבורה על קבוצה“, והוא בא לבטא את הקשר בין חבורות לבין סימטריות של אובייקטים שונים.

Delone sets are generalizations of point lattices: unformly discrete point sets with no large holes. In 1997 Gromov asked whether any Delone set in the Euclidean plane is bilipschitz equivalent to the integer lattice $Z^2$. A simpler but stronger condition than bilipschitz equivalence is bounded distance equivalence. So it is natural to ask which Delone sets in $R^d$ are bounded distance equivalent to (some scaled copy of) $Z^d$. This talk gives a gentle introduction to the problem and presents recent results in this context, mostly for cut-and-project sets on the line. In particular we show a connection between bouded remainder sets and cut-and-project sets that are bounded distance equivalent to some lattice.