2023 Bridges Conference Art Exhibition

# Benjamin David Grimmer

## Artists

## Statement

I am an optimizer. I do research in optimization, searching over every point in a shape to find the best one (by some definition and rigor). I teach optimization and find that drawing chalk pictures of the shapes we optimize over does not do justice to the math underneath. Much more beautiful (and mathematically insightful) shapes take care and planning. I typically 3D print these to use in class and research talks and to inspire my students. (I also do it because I find it fun)

## Artworks

This work physically represents a collection of open research questions, displaying 49 induced matrix norms mapping from L_p to L_q for various p and q. The difficulty in computing these norms varies:
For some values of p and q, a simple formula works (having a green base marked Polynomial on the shelf).
For some values, computing the norm is NP-Hard (having red/orange bases, marking them with citations to the paper that proved it).
Most surprisingly, for some values of p and q, we do not know (these norms are printed in gold as open questions).
When someone proves which category a golden norm belongs to, I'll send them the current golden ball and print a white one along with a colored base citing their result.