Tiling Space and Making Hard Problems Harder

  • Speaker
  • Mark Braverman, Ph.D.Professor, Department of Computer Science, Princeton University
Date & Time


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Simons Foundation Lectures are free public colloquia related to basic science and mathematics. These high-level talks are intended for professors, students, postdocs and business professionals, but interested people from the metropolitan area are welcome as well.
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A shape can tile space if we can take infinitely many copies of the shape and shift them around to cover every point without overlapping. For example, squares and hexagons can tile a plane, but circles can’t. Questions linger, though. What is the smallest surface area a tile may have? Does the answer change if we require the tiles to be symmetric?

In this lecture, Mark Braverman will discuss the question of minimizing the surface area of tiles, a problem that dates back to the 19th century. The question turns out to have surprising connections to computational complexity theory in the context of combining computationally difficult problems to make them even harder. Braverman will elucidate these connections and present results on the minimum surface area problem.

About the Speaker

Braverman is a professor at Princeton University. He works primarily on building new connections between theoretical computer science and other disciplines, including information theory, game theory, dynamical systems, analysis and geometry. He received a 2016 European Mathematical Society Prize and a 2019 NSF Alan T. Waterman Award.

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