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The Langlands program: a synthesis of number theory and representation theory.

Presented byÌý2024 Mahler Lecturer ProfessorÌýMatthew EmertonÌý(University of Chicago)

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.

The talk will be followed by a networking reception.

2024 Mahler Lecturer

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.

, running from 24 June-29 July.Ìý

About the speaker

Matthew Emerton is the 2024 Mahler Lecturer. HeÌýis 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.

Venue

The talk will be presented in the UNSW School of Mathematics and Statistics, Room 4082/4083 on level 4 of the Anita B. Lawrence Centre (East).

The School of Mathematics and Statistics is accessible via the Centre Wing or East Wing entrances to the building (campus map ref: H14 - H15).

*Please note that the School of Mathematics and Statistics is not accessible via the West Wing of the building.