The theory of numbers: From ancient Greece to the 21st century

Mahler Tour 2024 Public Lecture
SMRI was lucky enough to host esteemed number theorist Professor Matthew Emerton for a public lecture, as part of his Mahler Lecture Tour. This lecture, aimed at members of the public interested in mathematics, explained 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, Matthew Emerton sketched 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.  The focus emphasized how symmetries of mathematical problems, some obvious but some not-so-obvious, play a hidden role in the nature of their solutions.

Speaker bio: 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 International Congress of Mathematicians.

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.

In addition to researching mathematics and advising his own students, Professor Emerton enjoys walking and kayaking in Chicago with his wife Therese (weather permitting!), reading poetry, and long-distance running.