AIM Seminar: Interleaved group products
Speaker: Emanuele Viola (CCIS, Northeastern University)
Abstract: Let G be the special linear group SL(2,q). We show that if (a1,a2) and (b1,b2) are sampled uniformly from large subsets A and B of G^2 then their interleaved product a1 b1 a2 b2 is nearly uniform over G. This extends a result of Gowers (2008) which corresponds to the independent case where A and B are product sets. We obtain a number of other results. For example, we show that if X is a probability distribution on G^m such that any two coordinates are uniform in G^2, then a pointwise product of s independent copies of X is nearly uniform in G^m,
where s depends on m only. Similar statements can be made for other groups as well. (Results obtained with Timothy Gowers.)
These results have applications in computer science, which is the area where they were first sought by Miles and Viola (2013).
Tuesday, March 20 at 11:00am to 12:00pm
Northeastern University, 511 Lake Hall