## AMUSE

**Date: ** April 4, 2024

**Time: ** 6:00PM - 7:00PM

**Location: ** BLOC 306

**Speaker: **Dr. Guy Battle, Texas A&M University, Mathematics

**Title: ***Nano-Electric Crystal Ball Calculation as a Problem in Number Theory*

**Abstract: **Consider nano-crystals based on an arbitrary salt compound (with no regard for whether the technology for creating a chosen shape even exists). We pursue the problem of calculating the net electric charge due to a difference between the number of alkali ions and the number of halogen ions. If the crystal has an I^infinity shape of arbitrary size, then the net charge is essentially zero - i.e., zero plus or minus the fundamental unit of charge. In the case where the crystal has an I^1 shape, we derive an expression for the net charge that has the same order of magnitude as the area of the surface for an arbitrarily large size. In the case where the crystal has an I^2 shape, the problem of calculating the net charge for an arbitrary radius seems to be open. We discuss a couple of partial results.