Before the lecture, there will be small refreshments outside the hall at 4 pm. During this time, you can discuss with each other and meet the speaker. 

Eva Miranda is Chair of Geometry and Topology at UPC in Barcelona and Director of the Lab of Geometry and Dynamical Systems. She has been awarded a Bessel Prize, the François Deruyts Prize by the Royal Academy of Sciences in Belgium, and is a two-time ICREA Academia awardee. She was named the 2023 London Mathematical Society Hardy Lecturer and the 2025 Gauss Professor at the University of Göttingen. She has also been a speaker at the 8th European Congress of Mathematics (8ECM) in Portorož. Her research explores the intricate connections between geometry, dynamical systems, and mathematical physics, with major contributions to singular symplectic manifolds, quantization, and undecidability in dynamical systems

Abstract

Will the 2024 YR4 asteroid strike Earth? Science’s answer: maybe. With a shifting probability, it could arrive dramatically on Christmas Eve 2032. Despite our reliance on mathematics and physics for precise predictions, history warns us that certainty is elusive.

David Hilbert once dreamed of a world where reason would conquer uncertainty, but Alan Turing shattered this vision with his proof of the undecidability of the halting problem. Chaos theory warns that even minor measurement errors can escalate into vast unpredictability. Celestial mechanics, once seen as deterministic, reveals a universe more chaotic than Newton had imagined.

Beyond classical chaos lies a deeper enigma—logical chaos. In 2021, collaborating with Robert Cardona, Daniel Peralta-Salas, and Francisco Presas, I demonstrated the existence of undecidable fluid paths—trajectories so complex that no logical framework can predict their evolution. Could similar undecidable phenomena exist in celestial mechanics? Are there cosmic events so complex that no theory, no supercomputer will ever decipher them?