I will explain how ideas familiar from the conformal bootstrap lead to new rigorous upper bounds on the spectral gap of the Laplacian on hyperbolic orbifolds. The bounds follow from a combination of representation theory and linear programming. In two dimensions, the bounds allow us to determine the set of spectral gaps attained by all hyperbolic orbifolds. I will also discuss the question of...
How to stack an infinite number of oranges to maximize the proportion of the covered space? Kepler conjectured that the "cannonball" packing is an optimal way to do it. This conjecture took almost 400 years to prove, and the proof of Hales and Ferguson consists of 6 papers and tens of thousands of lines of computer code.
Given an infinite number of coins of 3 fixed radii, how to place them...
Classifying perturbative fixed points near upper critical dimensions is crucial for understanding the space of conformal field theories and critical phases of matter. The one-loop beta functions for general scalar field theories are a set of polynomial equations. There are various mathematical approaches to solve these equations, including Buchberger’s algorithm to calculate the Gröbner basis...
