Tue, 14 Oct 2025
15:30
L4

Vafa-Witten invariants from modular anomaly

Sergey Alexandrov
(Montpelier)
Abstract
I'll present a modular anomaly equation satisfied by generating functions of refined Vafa-Witten invariants 
for the gauge group $U(N)$ on complex surfaces with $b_1=0$ and $b_2^+=1$, 
which has been derived from S-duality of string theory.
I'll show how this equation can used to find explicit expressions for these generating functions
(and their modular completions) on $\mathbb{CP}^2$, Hirzebruch and del Pezzo surfaces.
The construction for $\mathbb{CP}^2$ suggests also a new form of blow-up identities.
Schur multipliers of C⁎-algebras, group-invariant compactification and applications to amenability and percolation
 Mukherjee, C Recke, K Journal of Functional Analysis volume 287 issue 2 110468-110468 (01 Jul 2024)
Photo of Harry

Hyperconvex metric spaces - a case study by Harry Petyt

I work in the field of geometric group theory. This is a pretty broad heading, but for me it means that the goal is to understand infinite groups, and the strategy is to get them to act on nice metric spaces that we know a lot about. 

Short stories

It's a little-known fact that Fibonacci was a keen marathon runner.

Okay, he wasn't but he could be an invaluable help if you are a keen marathon runner.

Josh Bull is very keen.

Thu, 27 Nov 2025
16:00
Lecture Room 4

Irreducibility of polarized automorphic Galois representations in infinitely many degrees

Dmitri Whitmore
(University of Cambridge)
Abstract

It is well-known that one can attach Galois representations to modular forms. In the case of cusp forms, the corresponding l-adic Galois representations are irreducible for every prime l, while in the case of Eisenstein series, the corresponding Galois representations are reducible. The Langlands correspondence is expected to generalise this picture, with cuspidal automorphic representations always giving rise to irreducible Galois representations. In the cuspidal, polarized, regular algebraic setting over a CM field, a construction of Galois representations is known, but their irreducibility is still an open problem in general. I will discuss recent joint work with Zachary Feng establishing new instances of irreducibility, and outline how our methods extend some previous approaches to this problem.

STEM for Britain 2026

Early career STEM researchers are encouraged to take part in one of the UK’s most prestigious opportunities to showcase their research: a national poster competition held at the heart of Parliament. This event invites early-stage researchers in science, technology, engineering, and mathematics (STEM) to present their work to Members of both Houses, fostering direct engagement between academia and policymakers.

The finals of STEM for BRITAIN 2026 will be held in Parliament on 17 March 2026. 

Cafe π news - Fairtrade Fortnight

22 September to 5 October.

We use a wide range of Fairtrade products in the cafe including bananas, coffee, Clipper teas, Maltesers, Tony’s Chocolonely, Lemonaid and sugar.

Special Fairtrade Treat - Banana & Cinnamon Cake with White Chocolate, made in-house by our chefs with Fairtrade bananas, available across all our outlets for only £2.60.

Contrasting ecological patterns of Venezuelan equine encephalitis and Madariaga viruses in small mammal and mosquito populations from two enzootic regions of Panama
 Galue, J de Souza, W Torres-Cosme, R Lezcano-Coba, C Tesh, R Guzman, H Weaver, S Capitan-Barrios, Z Valderrama, A Samudio, R Vittor, A Vasilakis, N Carrera, L Donnelly, C Faria, N Carrera, J Vector-Borne and Zoonotic Diseases (29 Sep 2025)
Colloquium: The Cosmic Dipole Anomaly
 Von Hausegger, S mohayaee, R secrest, N rameez Sarkar, S Reviews of Modern Physics
Data-Driven Yet Formal Policy Synthesis for Stochastic Nonlinear Dynamical Systems
 Nazeri, M Badings, T Soudjani, S Abate, A Proceedings of Machine Learning Research volume 283 1550-1564 (01 Jan 2025)
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