Mon, 19 Oct 2026
16:00
C4

Hermitian duals and the local Langlands correspondence

Maximilien MacKie
(University of Oxford)
Abstract

The local Langlands correspondence is a conjectural relation between the representations of a p-adic group and its L-parameters (which one can think of as representations of a `dual' group). Given a representation, it is natural to construct the hermitian dual representation. In this talk we present an explicit conjectural local Langlands correspondence, beyond the tempered case and including enhancements. We then show, assuming this conjecture, that constructing the hermitian dual corresponds to twisting its enhanced L-parameter by the compact real form on the dual group, generalising a result of Adams and Vogan. If time permits we will also show that standard desiderata of the local Langlands correspondence are in fact equivalent to this compatibility with hermitian duals.

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Song of the Week 2: Sergei Rachmaninoff: Prelude in C♯ Minor

One of Rachmaninov's most famous pieces, this prelude, one of a set of five, was written when he was nineteen. Rachmaninov was himself a very accomplished pianist (he had very large hands which no doubt helped). He also loved fast cars and speedboats. 

And for the music buffs among you, on 16 January 1910 no lesser a figure than Gustav Mahler conducted Rachmaninov playing his own third piano concerto at Carnegie Hall, New York.

Tue, 08 Dec 2026
15:30

TBA

Yoav Len
(Mathematical Institute (University of St Andrews))
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Wed, 21 Oct 2026
01:00
Exceptionally, this seminar will take place in Classroom C2.

ADHM Bundles and counting surfaces in Calabi--Yau fourfolds

Noah Dizep
(Heriot-Watt University, Edinburgh)
Abstract
The recent seminal work by Bae, Kool and Park establishes a DT type theory counting surfaces in Calabi--Yau fourfolds. I will present on joint work with R. Szabo on computing a variant of surface counts on CY4s using Diaconescu--Piazzalunga's technology of ADHM Bundles and Coulomb branch localization on a smooth, toric, projective surface.
 
We compute these enumerative invariants by computing the partition function of a topologically twisted Gauge theory similar in nature to Vafa--Witten's twist of 4d N=4 SYM. 
 
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Micro-internships for Oxford students

Applications for the Micro-Internship Programme are open until 2 November 2026. The programme offers two- to five-day voluntary learning and development opportunities with a diverse range of organisations during weeks 9 and 10 of Michaelmas term.

Get Hired Programme

We have opened up a new Get Hired programme for accounting and finance students interested in graduate roles (2024 - 2027 graduates) and summer internships (2028 graduates looking for a 2027 summer internship). Both groups can apply via this form.

Morgan Stanley Event

At Morgan Stanley, we believe that meaningful careers are built through continuous learning, collaboration and the opportunity to make an impact. Our people are united by a shared commitment to excellence, strong  partnerships and helping clients, communities and one another succeed.

If you're curious about a career in Quantitative Finance and want to learn more about the opportunities available, we invite you to join us at the 

Meet and Greet our Strats – Oxford event

Annual Institute celebration

We will be holding our Annual Institute celebration on Monday 19th October 2026 from 5:00pm to approximately 7:00pm in Lecture Room 1 in the Andrew Wiles building. As part of the event, we will also be holding our Awards Ceremony, where we will celebrate the achievements of fellow students and our staff though the Examination Prizes and Departmental Teaching Prize Awards for the 2025 – 2026 academic year.

We are pleased to announce that there will also be a talk from Professor James Maynard.

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