MaLGa Colloquia - Imaging, Inverse Problems, and AI: Where Does the Mathematics Go?

Title

MaLGa Colloquia - Imaging, Inverse Problems, and AI: Where Does the Mathematics Go?

Speaker

Carola-Bibiane Schönlieb - University of Cambridge (UK)

Abstract

Mathematical imaging has long been a driver of fundamental developments across the mathematical sciences, rooted in the challenge of reconstructing and interpreting information from incomplete, noisy, or indirect data. This has led to deep connections with analysis, geometry, inverse problems, and probability, and has enabled transformative applications across science and engineering.

The rapid rise of artificial intelligence is now reshaping this landscape. Data-driven methods, in particular deep learning, achieve remarkable empirical performance in imaging tasks, yet they also raise fundamental questions about stability, generalisation, interpretability, and the role of prior knowledge and physical structure.

In this talk, I will argue that the central challenge is not to replace mathematical models with data, but to understand how data and structure interact. I will highlight recent developments that combine learning with geometry, physics, and variational principles, leading to new analytical frameworks and computational paradigms. From this perspective, imaging continues to act as a catalyst for mathematics—offering a fertile ground for developing the next generation of ideas at the interface of analysis, computation, and learning.

Bio

Carola-Bibiane Schönlieb is Professor of Applied Mathematics at the University of Cambridge. There, she is head of the Cambridge Image Analysis group. Since 2011 she is a fellow of Jesus College Cambridge. Her current research interests focus on variational methods, partial differential equations and machine learning for image analysis, image processing and inverse imaging problems, and the mathematical foundations of machine learning. 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.

Her research has been acknowledged by scientific prizes, among them the LMS Whitehead Prize 2016, the Philip Leverhulme Prize in 2017, the Calderon Prize 2019, a Royal Society Wolfson fellowship in 2020, a doctorate honoris causa from the University of Klagenfurt in 2022, and by invitations to give invited lectures at several renowned applied mathematics conferences, including SIAM, ICM and ICIAM. She is also a SIAM fellow, and ELLIS fellow and a fellow of the Academy of the Mathematical Sciences.

Carola graduated from the Institute for Mathematics, University of Salzburg (Austria) in 2004. From 2004 to 2005 she held a teaching position in Salzburg. She received her PhD degree from the University of Cambridge (UK) in 2009. After one year of postdoctoral activity at the University of Göttingen (Germany), she became a Lecturer at Cambridge in 2010, promoted to Reader in 2015, promoted to Professor in 2018, and elected to the Professorship of Applied Mathematics (2006) in 2025. Carola convened the European Women in Mathematics Association between 2016 and 2020 and chaired the Committee for Applications and Interdisciplinary Relations (CAIR) of the EMS from 2021 to 2025. She also has been holding several leadership positions at SIAM.

When

Monday, April 20th, 16:00

Where

Room 706, UniGe DIBRIS/DIMA, Via Dodecaneso 35