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2024-05-222024-07-22https://rhed.amsi.org.au/wp-content/uploads/sites/73/2020/06/amsi_rhed_v2-2.pngResearch and Higher Education200px200px

**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.

**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.

DATE | TIME | Lecture Type | TITLE | VENUE | STATE | Register | WATCH ONLINE |
---|---|---|---|---|---|---|---|

24 June | 5:30pm-6:30pm | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | The University of Sydney Sydney Nanoscience Hub (A31), Lecture Theatre 4002 (Messel) | NSW | Register Now | View Lecture Recording |

26 June | 2pm | Pure Maths Colloquium | The Langlands program: a synthesis of number theory and representation theory | UNSW Room: RC 4082 (Anita B. Lawrence Centre, formerly the Red Centre) | NSW | No Registration Required More Information | |

1 July | 12.30pm | Colloquium | Symmetries in number theory | University of Newcastle Room V-G10 | NSW | No Registration Required More information | |

4 July | 5:30pm - 6:30pm AEST | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | Australian National University Seminar room: 1.33 & 1.37 Mathematical Sciences Institute | ACT | Register Now | |

8 July | 11am-12.30pm | Colloquium | Symmetries in number theory | The University of Queensland Room: 67-442 | QLD | TBA | |

8 July | 6pm (Refreshments served from 5pm) | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | The University of Queensland Physiology Learning Theatre: 63-348 | QLD | Register Now | |

9 July | 2pm-3.30pm | Seminar | Recent developments in the Langlands program | The University of Queensland Room: 67-442 | QLD | ||

16 July | 3pm | Colloquium | Symmetries in number theory | Monash University Room 340, 9 Rainforest Walk, Monash Clayton Campus | VIC | More information | |

17 July | 5pm-6pm | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | The University of Melbourne JH Michell Theater, Peter Hall building | VIC | More information | |

19 July | 2pm-3pm | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | La Trobe University, TLC 311. Teaching and Learning Commons Building, and online | VIC | More information Zoom links to be distributed on request | |

23 July | 1pm-2pm | Graduate Student Talk | Modular forms and Galois representations | The University of Melbourne, Peter Hall Building, Room 162 | VIC | More Information Register Now | |

25 July | 2.15pm-4.15pm | Seminar | From modular curves to categorification | The University of Melbourne, Peter Hall Building, Room 162 | VIC | More Information Register Now | |

29 July | 6pm -7 pm | Public Lecture | The theory of numbers, from ancient Greece to the 21st century | University of Western Australia, Fox Lecture Hall, 35 Stirling Hwy, Crawley | WA | Register Now Or email ias@uwa.edu.au for more information | |

*all times will be in host local time |

**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.

- 2022: Professor Frank Calegari, The University of Chicago
- 2019: Dr Holly Krieger, The University of Cambridge
- 2017: Professor Ivan Corwin, Columbia University
- 2015: Professor Manjul Bhargava, Princeton University
- 2013: Professor Akshay Venkatesh, Stanford University
- 2011: Professor Peter Sarnak, Princeton University
- 2009: Professor Terence Tao, UCLA
- 2007: Professor Mark Kisin, University of Chicago
- 2005: Professor Bruce E. Berndt, University of Illinois Urbana-Champaign

More information: austms.org.au/meetings/mahler-lecture-tour