Vincent Grande
Computational Network Science@RWTH Aachen University
I am a third-year PhD Candidate in the Computational Network Science Group of Michael Schaub and a member of the RTG UnRAVeL (Research Training Group for Uncertainty and Randomness in Algorithms, Verification, and Logic).
My research deals with the analysis of networks and data sets with higher-order information. A central motive is to use a blend of techniques from algebra, topology, homotopy theory, and network science to explore the relationship between small-scale connectivity data and other localised information, and large-scale behaviour and global properties of data sets.
If you are interested in my research and have questions, new ideas, or suggestions, feel free to get in touch! :)
Short CV
Before moving to Aachen, I obtained a Master of Science in Pure Mathematics at the University of Bonn and a Master of Advanced Study at the University of Cambridge, UK, both times focussing on homotopy theory, algebraic topology, and discrete mathematics. Prior to that, I did a Bachelor of Science in Pure Mathematics and a Two-Subjects Bachelor of Arts in Philosophy/Mathematics at the University of Göttingen focussing on algebra and Wittgenstein’s philosophy of language.
I wrote my Master’s thesis on G-global homotopy theory supervised by Stefan Schwede, my Cambridge Part III essay on Bott periodicity and the J-homomorphism supervised by Oscar Randal-Williams, and my Bachelor’s thesis on exact modules over Manuel Köhler’s ring supervised by Ralf Meyer.
news
| Oct 28, 2024 | I’ll be at the 2024 Asilomar Conference on Signals, Systems, and Computers from 27 to 30 October! On Monday, I will be giving a talk in the session for Topological Signal Processing and Learning on my newest project, topological trajectory prediction. In particular, I will talk about how to infer the underlying topology of a higher-order network from potentially unlabelled trajectory data. |
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| Sep 20, 2024 | I’ll give a talk at the Mathematics Lab Seminar at the Max Planck Institute for Mathematics in the Sciences in Leipzig on “Hodge Learning: Relating global topology and local features of point clouds.” |
| Aug 07, 2024 | I’ll be at SPIRES at the Centre for Topological Data Analysis at the University of Oxford from August 7 to 9. I’ll present a poster on my paper on Non-isotropic persistent homology. |
| Jun 25, 2024 | I just gave a talk on Hodge Learning and my ICASSP 2024 Paper at the Graph Signal Processing Workshop 2024 in Delft. |
| Jun 16, 2024 | I’ll be at NetSci from June 16 to 21. I am excited to give a talk at HONS@NetSci on 18 June on “Hodge Learning: What the Eigenspectrum of the Hodge Laplacian tells us about higher-order network topology and geometry”. I’ll also be presenting a poster.   |
| Jun 13, 2024 | I’ll be giving a talk on Topological Point Cloud Clustering and Representations at the Helmholtz AI Conference in Düsseldorf.  |
| Jun 06, 2024 | I have released my first python package topf, which computes topological point features in point clouds based on our recent article. The code and many examples are available here . Alternatively, install Julia and Python and simply run pip install topf.  |
| Jun 05, 2024 | A preprint to my new joint with Michael Schaub paper “Node-Level Topological Representation Learning on Point Clouds” is now available on arxiv! We construct point-level features vectors quantifying the contribution of the points to the global shape and properties of the point cloud. |
| Apr 24, 2024 | I’ll be at the WINQ workshop on Dynamics and Topology of Complex Network Systems at Nordita in Stockholm from 29 April to 2 May. On Wednesday, I’ll give a talk about relating local features and global topology of networks and point clouds: Learning from the harmonic spaces of Hodge-Laplacians. |
| Apr 14, 2024 | I’ll be at ICASSP 2024 from 14 to 19 April in Seoul   ! I will be presenting our ICASSP paper “Disentangling the Spectral Properties of the Hodge Laplacians: Not All Small Eigenvalues Are Equal.” on Thursday. For a musical version of figure 2, click here! |
| Mar 26, 2024 | The code for our paper on disentangling the spectral properties of Hodge Laplacians in filtrations is now available on gitlab! We provide many new cool tools related to exploring the eigenvalue and -vector spectrum of Hodge Laplacians across filtrations of simplicial complexes. |
| Dec 20, 2023 | “Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal” has just been accepted at ICASSP 2024, the International Conference on Acoustics, Speech and Signal Processing. In the joint article with Michael Schaub we attempt to “track” eigenvectors of the Hodge Laplacian through the filtration of a simplicial complex, bridging TDA and Topological Signal Processing. And we have many pictures! |
| Nov 28, 2023 | How to make sense of the vast spectral information of the Hodge Laplacian? “Disentangling the Spectral Properties of the Hodge Laplacian: Not All Small Eigenvalues Are Equal”, a new preprint of my joint article with Michael Schaub is now available on arXiv. |
| Nov 24, 2023 | My article with Michael Schaub on Non-isotropic Homology just got accepted to the 2nd Learning on Graph Conference! Feel free to drop by my poster at the poster session! |
| Oct 26, 2023 | Is there one ‘correct’ metric for Persistent Homology, or should we rather analyse and compare multiple metrics on point clouds at once? We change the metric, track the effects on the persistence diagrams and extract new information on orientation and orientational variance and strength of point clouds! A preprint of my joint article with Michael Schaub on Non-isotropic Homology is now available on arXiv. |
| Jul 26, 2023 | I just uploaded the new extended abstract on Non-Isotropic Persistent Homology, which I will be presenting on Friday at the TAG-ML Workshop @ ICML2023. Check it out here! |
| Jun 20, 2023 | The code for both Topological Point Cloud Clustering and Restarting Strategies on Markov Chains is now publicly available. |
| Jun 18, 2023 | Our extended abstract on Non-Isotropic Persistent Homology together with Michael Schaub has been accepted for a poster presentation at the workshop on Topology, Algebra, and Geometry in ML @ICML 2023. See you in Hawaii. |
| Apr 25, 2023 | Topological Point Cloud Clustering, my favourite paper I wrote so far, got accepted at ICML 2023! |
| Apr 24, 2023 | Two articles got accepted for publication! The paper on paper Restarting Strategies on Partially Observable Markov Chains got accepted at ICALP 2023, and Signal Processing on Product Spaces got accepted for ICASSP 2023. |
| Apr 10, 2023 | A preprint of my joint article with Michael Schaub on Topological Point Cloud Clustering is now available on arXiv. Very many colourful pictures, figures, and some cool new ideas! |
| Mar 21, 2023 | A preprint of my joint paper with Mitch Roddenberry, Florian Frantzen, Michael Schaub, and Santiago Segarra on Signal Processing on Product Spaces is now on arxiv!  (There is a connection to oceans!) |
| Mar 07, 2023 | A preprint of my paper on Restarting Strategies on Partially Observable Markov Chains together with Javier Esparza is now available on arXiv. |
| Feb 22, 2023 | Launch of the new website. I still don’t have much to show here, but anyway, a website is a website. |
| Nov 09, 2022 | Gave a talk at the UnRAVeL bi-weekly seminar on restart strategies on partially observable Markov chains. |
| Nov 04, 2022 | Co-organised the joint workshops of the research training groups UnRAVeL and LogiCS a TU Vienna. Wonderful opportunity to visit Vienna! |
| Jul 22, 2022 | I had a great time visiting the research group of Javier Esparza at TU Munich for a week, working on restart strategies for partially observable Markov chains. |
| Jun 01, 2022 | Workshop of my Research Training Group in Vaals. I somehow managed to come out on top at the beer tasting challenge. I always knew that doing a PhD uncovers hidden abilities… |
| Apr 01, 2022 | I just started my PhD and I am a Computer Scientist now. How exciting! |
