Title: Dimension of sumsets of restricted digit Cantor sets in the integers
Speaker: Daniel Glasscock
Speaker Info: Northeastern University
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Abstract:
Harry Furstenberg made a number of conjectures in the 60's in seeking to make precise the heuristic that there is no common structure between digit expansions in distinct prime bases. While the famous x2, x3 conjecture in ergodic theory remains unsolved, recent solutions to conjectures of his concerning the dimension of sumsets and intersections of p- and q- invariant sets now shed new light on old problems. In this talk, I will explain how to use tools from fractal geometry and uniform distribution to determine the dimension of sumsets of restricted digit Cantor sets with respect to different bases in the integers. This talk is based on joint work with Joel Moreira and Florian Richter.Date: Tuesday, February 26, 2019