Geometric Intelligence Workshop 

9:30 Adele Myers - Geomstats Tutorial 1: Learning from Shapes Using Geomstats

Shapes are everywhere in nature. Therefore, quantifying differences between shapes is relevant for nearly every field. For simple shapes, this task is easy. For example, one can compare two circles by computing the difference between their radii. This question becomes much more difficult when the shape in question is more complicated, like a cell outline or brain surface. Here, we delve into the field of shape analysis and shape spaces, starting from the basic question of "what is a shape" and ending with a taste of Geomstats: a software package that makes computations in shape spaces accessible for people in all fields.

10:30 Luís Pereira - Geomstats Tutorial 2: Geomstats: a Python package for Riemannian Geometry and Geometric Statistics

Geomstats is an open-source Python package for computations, and statistics on nonlinear manifolds. We provide object-oriented and extensively unit-tested implementations. Manifolds can be equipped with Riemannian metrics with associated exponential and logarithmic maps, geodesics, and parallel transport. Some manifolds can also be endowed with additional mathematical structures, such as Lie group, or fiber bundle structures. Statistics and learning algorithms provide methods for estimation, clustering, and dimensionality reduction on manifolds. All associated operations are supported in different backends, namely NumPy, Autograd, and PyTorch. In this talk, we briefly introduce the main concepts in Riemannian geometry and discuss the package design.  We show that Geomstats provides reliable building blocks to both foster research in differential geometry and statistics and democratize the use of Riemannian geometry in statistics and machine learning. 

The source code is freely available under the MIT license at https://github.com/geomstats/geomstats.

11:30 ☕

12:00 Nina Miolane - Geometric Intelligence in Minds and Machines (Coloquio IMATE)

Neural representations in both biological and artificial neural networks reveal rich and intricate geometric structures. From the toroidal neural manifolds that shape navigation in animals and recurrent neural networks to the complex topological interactions among neurons in brains and machines, intelligence emerges within a landscape of geometries we are only beginning to explore. Even the higher layers of neural networks in computer vision—and the visual cortex itself—exhibit striking symmetries that challenge our understanding of learning and perception. 

In this talk, we delve into the mathematical foundations of neural representations and showcase ongoing research at the Geometric Intelligence Lab. By bridging geometry, neuroscience, and machine learning, we aim to expand the frontiers of how we understand and model intelligence—both artificial and biological—advancing fundamental science and transforming brain research and care.

13:00 lunch

15:00 Yalbi Balderas Martínez - Building a Multiscale Computational Framework to Address the Complexity of Respiratory Diseases

In this talk, we will discuss the process of developing a multiscale computational approach to study respiratory diseases by combining molecular, cellular, and tissue-level data. At the molecular level, we can use AlphaFold to explore protein structures—particularly transcription factors and membrane proteins—to better understand mechanisms involved in antibody response and disease progression. At the cellular level, single-cell transcriptomics allows us to investigate aging, cellular diversity, and interactions within lung organoids. Complementing this, our imaging team is working to generate high-resolution tomographic datasets that will support predictive modeling for early detection and patient care. Integrating such diverse data presents several challenges—from handling high-dimensional information and aligning outputs across methods, to ensuring that mathematical tools are meaningfully applied in a biomedical context. 

We will reflect on these ongoing challenges and how collaboration across disciplines is central to making this integration possible. Ultimately, our goal is to show how these approaches can contribute to better understanding disease complexity and supporting more accurate, personalized strategies in public health and clinical care.

16:00 Break 

16:15 Louisa Cornelis - Graphing the Proteome: A GNN Approach to Predict Disease Severity in Frontotemporal Dementia 

Recent advances in large-scale proteomics enable capture of thousands of proteins in human biospecimen samples, supporting discovery of disease-related biomarkers and drug targets. Traditional proteomic workflows model proteins as individual predictors of disease outcomes, failing to account for how relationships between proteins influence predictive performance. Here we present a novel analytical framework applying a biologically-inspired graph attention neural networks to cerebrospinal fluid proteomic data for predicting disease severity in 252 participants with frontotemporal dementia, a progressive neurodegenerative disease that lacks robust prognostic biomarkers. Protein data is formatted into disease specific co-expression graphs using weighted correlation network analysis. Graph attention layers are utilized to extract hierarchical protein module-level graph features, which are then used alongside patient level demographic data for downstream predictions. The framework successfully forecasts cognitive decline and gold-standard markers of neurodegeneration, surpassing traditional analytical methods including differential regression and LASSO regression. Through systematic network interpretation using feature attribution techniques, we identify proteins with high importance for disease severity prediction that are not detected by other approaches, including targets linked to neuroimmune signaling and sugar metabolism. 

Our study demonstrates how graph-based deep learning approaches can extract meaningful insights from high-dimensional proteomic data, advancing our understanding of the molecular underpinnings of frontotemporal dementia with potential applications for all neurodegenerative diseases.

16:40  Sarah Kushner - Exploring volume changes in the brain during pregnancy

There is an extreme lack of medical research on women. Most studies include male participants, leading to a deficit of important healthcare information for half of world’s the population. Pregnancy is an experience many women go through in their lifetime, yet there is little known about the effects of pregnancy on a woman’s brain. In our work, we aim to explore the changes in the brain on the first MRI dataset of its kind. We are trying to apply statistics on manifolds to predict whether an expecting mother will have post partum depression and design a digital twin of the brain over the course of a pregnancy.

9:30 Eduardo Velazquez Richards - Contour parametrization via anisotropic mean curvature flows

The evolution of curves by curvature-dependent flows has many applications, such as crystal growth modeling, interface dynamics, and fire propagation. In this talk, we present a parallelizable approach that couples a Poisson problem and a dynamic equation on the curve, along with the conditions ensuring an equivalence to the mean curvature flow. We also present a numerical implementation applied to the problem of contour parametrization of shapes in high-contrast pictures.

This is joint work with Pablo Suárez-Serrato

10:00 Víctor  Mijangos  - An adjacency-preserving sampling method for 3d surfaces processing with graph neural networks

This talk introduces a sampling method for 3D surfaces based on the EuLearn database, designed to preserve adjacency information. Maintaining adjacency is a crucial requirement for classifying topological invariants of surfaces. The proposed method samples points in an order induced by the spanning tree of the surface triangulation and subsequently generates a sphere for radial point sampling. Using this sampled data, various graph neural networks are applied to classify the genus of each surface. The results demonstrate that this sampling method effectively reduces the complexity of classification neural architectures while preserving essential topological information.

This is joint work with Rodrigo Fritz, Pablo Suárez-Serrato, Eduardo Velázquez Richards, Víctor Mijangos, and Anayanzi Martínez,

10: 30 Sergei Gukov - Math + AI = AGI

It comes as no surprise that solving challenging research-level math problems drives progress in mathematics. What is more surprising, though, is that solving such long-standing open problems also contributes to an entirely different field: the development of the next generation AI systems. 

We live in an exciting time where mathematics and AI can greatly benefit each other, and the goal of the talk is to explain how and why, drawing on specific examples from topology and combinatorial group theory.

11:30 ☕

12:00 Inicia Hackathón