Noah Giansiracusa

Experimental Study of Energy-Minimizing Point Configurations on Spheres

In this paper we report on massive computer experiments aimed at finding spherical point configurations that minimize potential energy. We present experimental evidence for two new universal optima (consisting of 40 points in 10 dimensions and 64 points in 14 dimensions), as well as evidence that there are no others with at most 64 points. We also describe several other new polytopes, and we present new geometrical descriptions of some of the known universal optima.

Conformal blocks and rational normal curves

We prove that the Chow quotient parametrizing configurations of n points in

Modular Interpretation Of A Non-Reductive Chow Quotient

\mathbb{P}^d

GIT Compactifications of

which generically lie on a rational normal curve is isomorphic to

M_{0,n}

\overline{M}_{0,n}

from Conics

, generalizing the well-known

GIT Compactifications of ℳ0,n from Conics

d = 1

The universal tropicalization and the Berkovich analytification

result of Kapranov. In particular,

A simplicial approach to effective divisors in

\overline{M}_{0,n}

\overline{M}_{0,n}

admits birational morphisms to all the corresponding geometric invariant theory (GIT) quotients. For symmetric linearizations the polarization on each GIT quotient pulls back to a divisor that spans the same extremal ray in the symmetric nef cone of