Vrije Universiteit Amsterdam, June 18, 2026.
Please register by clicking the link to the right.
Tentative schedule
10:00 – 10:50 Coffee, arriving
10:50 – 11:00 Welcome
11:00 – 11:45 Michael Lesnick (Albany, US)
11:45 – 12:30 Renate Roll (Nijmegen)
12:30 – 14:00 Lunch
14:00 – 14:45 Alejandro García Castellanos (U Amsterdam)
14:45 – 15:30 Hannah Santa Cruz Baur (VU Amsterdam)
15:30 – 15:45 Coffee
15:45 – 16:30 Marc van Kreveld (Utrecht)
16:30 – 18:00 Borrel
Organisers:
Abstracts:
Hannah Santa Cruz Baur:
Alejandro García Castellanos: Stitching neural networks through topology and geometry
This talk will briefly survey modern ways in which topological data analysis is integrated into machine learning and then focus on our work "Relative Representations: Topological and Geometric Perspectives" as a concrete example. To motivate relative representations, I will introduce the Platonic Representation Hypothesis: the idea that large self-supervised models trained on broad datasets, even across different modalities, tend to converge toward similar latent representations. This perspective motivates a popular technique in model stitching called Relative Representations, where latent spaces from different models are related through a simple transformation. In this talk, we introduce two principled improvements to this method grounded in topology and geometry: invariance to the parameter-space symmetries, and a topological regularization loss promoting higher similarity between networks. We demonstrate that both modifications improve stitching performance on natural language benchmarks, highlighting the practical value of topological data analysis in modern deep learning.
Mark van Kreveld: A sliding block puzzle
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 by 2 pieces on a hexagonal grid board of 2n+1 cells, using exactly n pieces, using sliding, turning and pivoting moves. This puzzle has a single empty cell on a board and forms a natural extension of the 15-puzzle or rush hour to include rotational moves. We analyze the puzzle and completely characterize the cases when the puzzle can always be solved. This is equivalent to asking when the collection of all placements of the pieces on the board forms a single connected component when sliding, turning and pivoting between different placements. We show that quadratically many moves (in n) are sometimes necessary and always suffice to reach a desired placement.
We also study the complexity of determining whether a given set of colored pieces can be placed on a colored hexagonal grid board with matching colors. We show this problem is NP-complete for arbitrarily many colors, but solvable in randomized polynomial time if the number of colors is a fixed constant.
Michael Lesnick: Density-sensitive bifiltrations in topological data analysis
The standard filtrations of TDA (Rips, Čech, Delaunay) are stable to small perturbations of the input data, but are notoriously unstable to outliers, and can be insensitive to variations in density. One of the main motivations of 2-parameter persistence is to address these limitations. There are several interesting ways one can define a density-sensitive bifiltration of point cloud or metric data, offering different tradeoffs between generality, computability, and robustness to outliers. Such bifiltrations have been actively studied in recent years, leading to substantial advances in our understanding of them, as well as new computational tools. In this talk, I will survey this progress.
Renate Roll: