Thu, 04 Jun 2026

14:00 - 15:00
Lecture Room 3

New results on the inclusion of closure orbits and bundles of matrices and matrix pencils

Prof Fernando De Teran
(University of Madrid Carlos III)
Abstract

Professor De Terran will talk about: 'New results on the inclusion of closure orbits and bundles of matrices and matrix pencils' 

Orbits of nxn matrices under similarity are sets of matrices with the same Jordan Canonical form (JCF). When computing the JCF (or just the eigenvalues) of a matrix, the knowledge of all possible JCFs of small perturbations of a given JCF can help to understand the output of the algorithm, which is affected by roundoff errors.

The JCFs that can be obtained after small perturbations of a given JCF, say J, correspond to orbits that ``dominate" the orbit of J. In other words, the orbit of J is in the closure of its dominant orbits. The hierarchy of orbit closures of general matrices is well-known, as well as that of the set of matrices with bounded rank.

For matrix pencils (namely, pairs of matrices with the same size) the inclusion relationship between orbit closures has been also considered since, at least the 1980's. In this case, the standard equivalence relation is the so-called strict equivalence, which preserves the eigenstructure of the pencil, and the canonical form for this relation is the Kronecker canonical form (KCF). The hierarchy of orbit closures of general pencils under strict equivalence is also well-known. However, when the pencil has some particular structure (e. g., symmetric or Hermitian) then we encounter a different problem if we want the perturbations to maintain this structure. Some effort has been devoted in recent years to the analysis of orbit closures of structured pencils.

In this talk, we will review some recent results on the inclusion relationship between orbit closures of general and bounded-rank structured matrix pencils. We will also consider the inclusion relation of bundle closures. Bundles are generalizations of orbits, allowing the eigenvalues to change, while keeping the KCF. 
 

 

Tue, 24 Feb 2026
15:30
L4

Deformations of schemes and derived categories

Samuel Moore
(Oxford)
Abstract

How much does the derived ($\infty$-)category of a scheme remember? In this talk, I will consider this question in the context of deformation theory and make precise the close relationship between the deformation theory of a scheme and its derived category. Along the way, I will also introduce some basics of derived deformation theory and pay special attention to mixed and positive characteristic phenomena. This talk is based on my recent work https://arxiv.org/abs/2512.24347.

Online Optimisation of Machine Learning Collision Models to Accelerate Direct Molecular Simulation of Rarefied Gas Flows
 Ball, N MacArt, J Sirignano, J Journal of Computational Physics volume 549 114601 (Mar 2026)
The Brauer–Manin obstruction for nonisotrivial curves over global function fields
 Creutz, B Voloch, J Rössler, D Algebra and Number Theory volume 20 issue 1 109-117 (01 Jan 2026)

Shorts stories 1 - Planets

You know those annoying social media films where a mic is shoved in front of a bunch of students and they're asked questions that have nothing to do with their studies or their lives, hoping they say something vaguely funny or interesting that might get a billion views on TikTok?

Register for Developing Academic Skills workshops

Colleagues are invited to register for the Centre for Teaching and Learning’s final two Developing Academic Skills workshops this academic year. The in-person sessions support colleagues involved in teaching or supporting undergraduate and postgraduate taught students’ academic skills development. Topics are structuring and editing (Monday 26 January), and developing exam and revision skills (Monday 23 February).

Hilary Term Planner for Careers and Employability

From application and interview support to sector insights and inspiring guest speakers, Hilary term offers a wide range of opportunities for students at every stage of career planning. Term planner highlights include the Creative Careers Festival in 4th week, the Crankstart and Diversity Fair in 7th week, and ongoing internship application support throughout the term.

Talk About Your Thesis

The Radcliffe Science Library invites science and medicine postgraduates to give a short, engaging 5–7 minute talk on their research. It’s a great chance to practice explaining your work clearly and succinctly - perfect preparation for the DPhil transfer or upcoming conferences - and to connect with other researchers in a relaxed setting. A complimentary pizza lunch will follow the talks.

Radcliffe Science Library , Friday 20 March 2026, 12:00–13:00 followed by lunch.

Fri, 23 Jan 2026
13:00
L6

Latschev’s theorem in persistent homotopy theory

Lukas Waas
(Oxford University)
Abstract
A central question in topological data analysis is whether the sublevel-set persistent homology of a function from a sufficiently regular metric space can be recovered from a finite point sample. A natural approach is to equip the Vietoris–Rips complex of the sample, at a fixed scale, with an appropriate filtration function and to compute persistent homology of the resulting filtered complex.
 
Despite its appeal, this approach has so far lacked theoretical guarantees. Existing results instead rely on image persistence, computing the image of transition morphisms between Rips homology at two different scales. By contrast, Latschev’s theorem in metric inference shows that, under suitable regularity and sampling assumptions, the Vietoris–Rips complex of the sample at a single scale is already homotopy equivalent to the underlying space.
 
In this talk, I will explain how tools from persistent homotopy theory yield a persistent version of Latschev’s theorem, which in particular resolves this classical question of estimating persistent homology at the level of persistent homotopy types.
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