In

2024 Mahler Lecturer

Professor Matthew Emerton, The University of Chicago

The Mahler lectures are a biennial activity organised by the Australian Mathematical Society, and supported by the Australian Mathematical Sciences Institute. The tour invites a prominent international mathematician to travel to Australian universities to deliver lectures at a variety of levels, including several public lectures.

Speaker

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.

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

Schedule

DATETIMELecture TypeTITLEVENUESTATERegister
24 June5:30pm-6:30pmPublic LectureThe theory of numbers, from ancient Greece to the 21st centuryThe University of Sydney
Sydney Nanoscience Hub (A31), Lecture Theatre 4002 (Messel)
NSWRegister Now
26 June2pmPure Maths ColloquiumThe Langlands program: a synthesis of number theory and representation theoryUNSW
Room: RC 4082 (Anita B. Lawrence Centre, formerly the Red Centre)
NSWNo Registration Required

More Information
1 July12.30pmColloquiumSymmetries in number theoryUniversity of Newcastle
Room V-G10
NSWNo Registration Required

More information
4 July5:30pm - 6:30pm AESTPublic LectureThe theory of numbers, from ancient Greece to the 21st centuryAustralian National University
Seminar room: 1.33 & 1.37
Mathematical Sciences Institute
ACTRegister Now
8 July11am-12.30pmColloquiumSymmetries in number theoryThe University of Queensland
Room: 67-442
QLDTBA
8 July6pm
(Refreshments served from 5pm)
Public LectureThe theory of numbers, from ancient Greece to the 21st centuryThe University of Queensland
Physiology Learning Theatre: 63-348
QLDRegister Now
9 July2pm-3.30pmSeminarRecent developments in the Langlands programThe University of Queensland
Room: 67-442
QLD
16 July3pmColloquiumSymmetries in number theoryMonash University
Room 340, 9 Rainforest Walk, Monash Clayton Campus
VICMore information
17 July5pm-6pmPublic LectureThe theory of numbers, from ancient Greece to the 21st century The University of Melbourne
JH Michell Theater, Peter Hall building
VICMore information
19 July2pm-3pmPublic LectureThe theory of numbers, from ancient Greece to the 21st centuryLa Trobe University,
TLC 311. Teaching and Learning Commons Building, and online
VICMore information

Zoom links to be distributed on request
23 July1pm-2pmGraduate Student TalkModular forms and Galois representationsThe University of Melbourne, Peter Hall Building, Room 162
VICMore Information

Register Now
25 July2.15pm-4.15pmSeminarFrom modular curves to categorificationThe University of Melbourne, Peter Hall Building, Room 162
VICMore Information

Register Now
29 July6pm -7 pmPublic LectureThe theory of numbers, from ancient Greece to the 21st centuryUniversity of Western Australia, Fox Lecture Hall, 35 Stirling Hwy, CrawleyWARegister Now

Or email ias@uwa.edu.au for more information
*all times will be in host local time

Talk abstracts

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.

Colloquium: Symmetries in number theory

Symmetries play a fundamental role in mathematics. I will begin by recalling two basic contexts in which symmetries occur:  symmetries of equations (Galois theory) and symmetries of harmonic analysis (discrete groups acting on symmetric spaces). I will then outline how the Langlands program conjectures a framework in which these two contexts are fundamentally related. While I will try to indicate some interesting contemporary results, my main focus will be on providing an introduction to the underlying ideas through simple but key examples.

Pure Maths Colloquium: The Langlands program:  a synthesis of number theory and representation theory

The Langlands program posits the existence of fundamental connections between symmetries of algebraic equations (Galois groups of algebraic number fields) and representation of Lie groups arising from harmonic analysis on symmetric spaces. I will try to explain some of the key ideas underlying these connections, with a focus on illustrative examples that are also related to important contemporary developments.

Pure Maths Seminar: Recent developments in the Langlands program

In this seminar I will explain some recent developments in the Langlands program that are of a “categorical” nature, to the effect that (at least conjecturally), various categories of representations of p-adic Lie groups can be realized inside categories of coherent sheaves on parameter spaces of Galois representations. In slightly different terms, this amounts to realizing modules over certain non-commutative rings as coherent sheaves on interesting geometric spaces. The focus of the talk will be on outlining the overall ideas, and then illustrating them through some interesting but accessible examples.

Graduate Student Talk: Modular forms and Galois representations

This is a pre-talk for the From modular curves to categorification talk aimed at graduate students.

I will begin by recalling the basic facts about Tate modules of elliptic curves. Building on this discussion, I will recall the basic facts about Galois representations attached to modular forms, and sketch the proofs of some of them.

Colloquium: From modular curves to categorification

The categorical form of the local Langlands correspondence conjectures (and in some cases proves) that derived categories of smooth representations of p-adic reductive groups can be realized inside the derived categories of coherent sheaves on suitable moduli spaces of Langlands parameters. The goal of this lecture is to motivate this categorical local Langlands conjecture from an arithmetic point of view, with the cohomology of modular curves as the starting point.

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2024 Mahler Lecture Series
2024 Mahler Lecture Series