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)
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).
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.
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
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.