19th Colloquium EHU - BCAM
Date: Wed, Nov 19 2025
Hour: 11:45 - 15:00
Location: Sala Aketxe – Edificio Sede at University of the Basque Country (UPV/EHU), Leioa
Speakers: Cornelia Drutu (University of Oxford) and Carola Bibiane Schönlieb (University of Cambridge)
11:45-12:45 | Prof. Cornelia Drutu: Connections between special classes of finite graphs and actions of infinite groups on Hilbert spaces
The talk will explain how two opposite properties of finite graphs turn out to be closely connected with two key properties of infinite groups, formulated in terms of actions on Hilbert spaces. Thus, expander graphs (graphs that are hard to disconnect, representing robust networks) are closely related with Kazhdan's property (T), a property of infinite groups describing their incompatibility with the geometry of Hilbert spaces, satisfied for instance by most linear arithmetic groups and by random groups with many relators. At the opposite end, median graphs (economic networks) are closely related with the property of a-T-menability (also called the Haagerup property), satisfied by amenable groups (in the sense of von Neumann) and by random groups with few relators, and implying the Baum-Connes conjecture.
13:00-14:00 | Lunch
14:00-15:00 | Prof. Carola-Bibiane Schöenlieb: Mathematical Imaging in the Era of AI
Imaging has long been a driving force for advances in mathematics. Central challenges in mathematical imaging connect naturally to functional and numerical analysis, nonlinear partial differential equations, inverse problems, statistical modelling and optimisation. Applications are wide-ranging, from biomedical and materials imaging to astronomy, the digital humanities, and technologies such as autonomous driving and medical diagnostics. The recent surge of AI has profoundly reshaped the landscape of imaging science. Data-driven methods, and in particular deep neural networks, have become the gold standard for many imaging tasks, demonstrating unprecedented accuracy in capturing and reconstructing information from data. Yet, their black-box nature raises important questions of stability, interpretability, and reliability.
In this talk, I will share my perspective on mathematical imaging as a fertile ground for mathematics research. I will discuss opportunities and challenges brought by AI, with a particular focus on structure-preserving deep learning and its potential for solving large-scale inverse imaging problems in a principled way.
Confirmed speakers:
Prof. Cornelia Drutu (University of Oxford) is Full Professor at the University of Oxford. She earned her PhD in Mathematics from the University of Paris-Sud (now Paris-Saclay), under the supervision of Pierre Pansu. She held visiting positions at the Max Planck Institute for Mathematics in Bonn, the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, the Mathematical Sciences Research Institute (currently the Simons-Laufer Institute) in Berkeley, California. She visited the Isaac Newton Institute in Cambridge as holder of a Simons Fellowship.
From 2013 to 2020 she chaired the European Mathematical Society/European Women in Mathematics scientific panel of women mathematicians. In 2009, she was awarded the Whitehead Prize by the London Mathematical Society for her work in geometric group theory. In 2017, she was awarded a Simons Visiting Fellowship. In 2023, she was the twelfth Emmy Noether Guest Professor at the University of Göttingen, Germany.
Professor Schönlieb is Professor of Applied Mathematics at DAMTP and head of the Cambridge Image Analysis group (CIA). Moreover, she is the Director of the Cantab Capital Institute for the Mathematics of Information (CCIMI) and Director of the EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging (CMIH), a Fellow of Jesus College, Cambridge and co-Chair of the Cambridge Centre for Data Driven Discovery (C2D3). Currently she is also chairing the SIAM activity group on Imaging Sciences and the Applied Mathematics Committee of the European Mathematical Society (EMS).
Professor Schönlieb's research interests focus on variational methods, partial differential equations and machine learning for image analysis, image processing and inverse imaging problems. She has active interdisciplinary collaborations with clinicians, biologists and physicists on biomedical imaging topics, chemical engineers and plant scientists on image sensing, as well as collaborations with artists and art conservators on digital art restoration.