NYU Mathematics Society (Math club) meets most Tuesday's 5:15pm — 6:30pm in 201 Warren Weaver Hall. We host faculty and student talks and discussions open to all undergraduate and graduate students.

Talks

February 23rd — TBA

February 16th — On Particles and PDE: From the Microscopic World to the Observable World

Professor Mark Wilkinson

Abstract: As we are all aware, matter in the Universe is made up of atoms (and those atoms themselves are made up of more “elementary” particles!), and this presents a challenge to the mathematician who wishes to model the Universe in an atomic way. For instance, the typical glass of water contains around 10^25 atoms of hydrogen and oxygen. When modelling this system with Newton's equations of motion, this gives rise to a coupled system of ODE for around 10^25 unknown quantities! Wouldn't it be nicer if we could replace this massive collection of equations with maybe one or two equations, whose solutions still tell us something meaningful about the original system of particles?

This is the question I'll address in this talk. But I'll be addressing these questions as a mathematician, not as a physicist! It might seem surprising, but there is a great deal of beautiful mathematics waiting in such physical problems. I hope to convince some of you that there is intrigue and glory to be found in this fascinating area of mathematics.