Week 1 Student Bulletin

Maths Institute

 

It's the Week 1 Student Bulletin! 

We hope you've had a good first week of term, and are looking forward to the year.

Short stories 2

9 am, first day of term, first lecture for our first-year undergraduates in the company of James Munro. The only time they'll turn up (vaguely) on time.

[Firstday]

 

Wellbeing at the Radcliffe Science Library

Take a well-deserved break and boost your wellbeing at the Radcliffe Science Library. Our wellbeing programme offers engaging and relaxing activities to help you unwind and connect with others. Build yourself up with Lego Lunch every Wednesday, or drop by for free hot drinks on Wednesday mornings during term time. If something’s on your mind, share it anonymously in our Worry Box or warm yourself up with a free Hot Chocolate.

Are you new to teaching at Oxford this year?

New tutors and teaching staff are encouraged to work through the Centre for Teaching and Learning’s Starting to Teach at the University of Oxford self-guided Canvas course (SSO required). The resource introduces the structure of teaching and learning at Oxford and includes modules on University resources, tutorial teaching, research supervision, and further support. It also includes a glossary to help you navigate some of the Oxford-specific terms you are likely to encounter.

On the parallels between minimal surfaces and Einstein four-manifolds
 Beard, M (06 Aug 2025)
Fri, 24 Oct 2025
13:00
L6

Generalized Persistent Laplacians and Their Spectral Properties

Arne Wolf
(Imperial College)
Abstract
Laplacian operators are classical objects that are fundamental in both pure and applied mathematics and are becoming increasingly prominent in modern computational and data science fields such as applied and computational topology and application areas such as machine learning and network science. In our recent paper, we introduce a unifying operator-theoretic framework of generalized Laplacians as invariants that encompasses and extends all existing constructions, from discrete combinatorial settings to de Rham complexes of smooth manifolds. Within this framework, we introduce and study a generalized notion of persistent Laplacians. While the classical persistent Laplacian fails to satisfy the desirable properties of monotonicity and stability - both crucial for robustness and interpretability - our framework allows to isolate and analyze these properties systematically.  We demonstrate that their component maps, the up- and down-persistent Laplacians, satisfy these properties individually. Moreover, we provide a condition for full monotonicity and show that the spectra of these separate components fully determine the spectra of the full Laplacians, making them not only preferable but sufficient for analysis. We study these questions comprehensively, in both the finite and infinite dimensional settings. Our work expands and strengthens the theoretical foundation of generalized Laplacian-based methods in pure, applied, and computational mathematics.


 

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