A note on indefinite matrix splitting and preconditioning
Wathen, A Linear Algebra and its Applications (23 Apr 2025)

The old mathematical ones are the best. Surprisingly popular on social media given you might actually need some maths to get it. Actually, not surprising at all.

Here's Vishal.

A one-mile road run open to the general public celebrating Roger Bannister’s historic achievement of breaking the mile world record in Oxford on May 6th, 1954.

Open to participants of all ages and abilities. Enter as an individual or as a team (including departmental teams).

Full info for the 5th May event

The popular annual programme is now open for registrations. From 12–16 May 2025, there'll be a week of events, activities, and learning opportunities, for anyone across the University who wants to get involved.

Find out more

The Language Centre has its usual array of courses this term. Enrolment for Trinity term is open until 12 noon on Wednesday of Week 1 (30 April). Classes take place weekly, online or in person, with many lunchtime and evening sessions on offer.

More details

Thu, 08 May 2025
12:00
C6

Sard properties for polynomial maps in infinite dimension

Daniele Tiberio
(University of Padova)
Abstract

Sard’s theorem asserts that the set of critical values of a smooth map from one Euclidean space to another one has measure zero. A version of this result for infinite-dimensional Banach manifolds was proven by Smale for maps with Fredholm differential. However, when the domain is infinite dimensional and the range is finite dimensional, the result is not true – even under the assumption that the map is “polynomial” – and a general theory is still lacking. In this seminar, I will provide sharp quantitative criteria for the validity of Sard’s theorem in this setting, obtained combining a functional analysis approach with new tools in semialgebraic geometry. As an application, I will present new results on the Sard conjecture in sub-Riemannian geometry. Based on a joint work with A. Lerario and L. Rizzi.

Localized tension-induced giant folding in unstructured elastic sheets
Guo, K Sune Simon, M Kwok, M Hsia, J Liu, M Vella, D Proceedings of the National Academy of Sciences volume 122 issue 20 (12 May 2025)
Tue, 03 Jun 2025
13:00
L2

Finite-temperature quantum topological order in three dimensions

Curt von Keyserlingk
(KCL )
Abstract

We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature--it therefore constitutes a quantum topological order at finite temperature. The model of interest is known as the fermionic toric code, a variant of the usual 3D toric code, which admits emergent fermionic point-like excitations. The fermionic toric code, importantly, possesses an anomalous 2-form symmetry, associated with the space-like Wilson loops of the fermionic excitations. We argue that it is this symmetry that imbues low-temperature thermal states with a novel topological order and long-range entanglement. Based on the current classification of three-dimensional topological orders, we expect that the low-temperature thermal states of the fermionic toric code belong to an equilibrium phase of matter that only exists at nonzero temperatures. We conjecture that further examples of topological orders at nonzero temperatures are given by discrete gauge theories with anomalous 2-form symmetries. Our work therefore opens the door to studying quantum topological order at nonzero temperature in physically realistic dimensions.

Tue, 10 Jun 2025
13:00
L1

A new construction of c=1 Virasoro blocks

Andy Neitzke
(Yale)
Abstract

I will describe a new method for constructing conformal blocks for the Virasoro vertex algebra with central charge c=1, by "nonabelianization", relating them to conformal blocks for the Heisenberg algebra on a branched double cover. The construction is joint work with Qianyu Hao. Special cases give rise to formulas for tau-functions and solutions of integrable systems of PDE, such as Painleve I and its higher analogues. The talk will be reasonably self-contained (in particular I will explain what a conformal block is).

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