Abstract: This talk will describe surprising applications of the theory of computing to questions in mathematical analysis. In particular, I will explain how algorithmic information theory can be used to remove structural hypotheses from prominent classical theorems in geometric measure theory. These include Marstrand's slicing theorem, Marstrand's projection theorem, and a characterization of packing dimension in terms of product sets.

Short Bio: Neil Lutz is an affiliate assistant professor at Iowa State University. His research interests include game theory, algorithmic information theory, and fractal geometry. Previously, he was a postdoctoral researcher and lecturer at the University of Pennsylvania and a lecturer at Iowa State University. He completed his Ph.D. at Rutgers University in 2017, on the topic of 'Algorithmic Information, Fractal Geometry, and Distributed Dynamics,' advised by Rebecca Wright.