AMSI MAHLER PUBLIC LECTURE TOUR HOSTED BY THE UQ SCHOOL OF MATHEMATICS & PHYSICS: PROFESSOR MATTHEW EMERTON - THE THEORY OF NUMBERS - FROM ANCIENT GREECE TO THE 21ST CENTURY

Public Lecture: The theory of numbers, from ancient Greece to the 21st century

This lecture, aimed at members of the public interested in mathematics, will explain some of the key ideas in the theory of numbers, as developed over the last two thousand-plus years. Beginning with the theory of geometric constructions from ancient Greek geometry, and its relationship to the discovery and properties of irrational numbers, I will sketch in broad outlines how these ideas evolved, through the theory of equations and their symmetries as developed by Galois, culminating in a description of some of the contemporary aspects of the theory. My focus will be on emphasizing how symmetries of mathematical problems, some obvious but some not-so-obvious, play a hidden role in the nature of their solutions.

Professor Matthew Emerton

The University of Chicago

Matthew Emerton is a Professor in the Department of Mathematics at the University of Chicago. He received his PhD from Harvard in 1998, under the supervision of Professor Barry Mazur. Following a postdoc at the University of Michigan, and an Assistant Professorship at the University of Chicago, he spent ten years as a faculty member at Northwestern University before returning to Chicago in 2011. He was an invited speaker at the 2014 ICM.

Professor Emerton’s areas of research are number theory, arithmetic geometry, and representation theory. He is known for his work on the Fontaine–Mazur conjecture, and for his construction (with Professor Toby Gee of Imperial College) of the eponymous Emerton–Gee Stacks, higher dimensional algebro-geometric objects which parameterize local Galois representations. Professor Emerton’s research is funded in part by both the National Science Foundation and the Simons Foundation.