In combinatorics and ergodic theory, the decomposition into structured and random objects has been successfully exploited to prove density results and refinements. In both fields, nilsystems are the model for structured configurations. Recently, Kra, Moreira, Richter, and Roberson used dynamics in nilsystems to provide a density version of Hindman's theorem. In this talk, we delve into further sumset consequences for these two extreme cases and provide some examples of applications.
","image_description":"","creation_date":"2026-05-26T10:23:46","last_modification_date":"2026-05-26T10:25:57","link_label":"","link_url":"","canceled":"False","cancel_reason":"","place_and_room":"CM 1 517","url_place_and_room":"https://plan.epfl.ch/?room==CM%201%20517","url_online_room":"","spoken_languages":["https://memento.epfl.ch/api/v1/spoken_languages/2/?format=json"],"speaker":"Tristán Rádić (Northwestern University)","organizer":"","contact":"Felipe Hernandez Castro","is_internal":"False","theme":"","vulgarization":{"id":3,"fr_label":"Expert","en_label":"Expert"},"registration":{"id":3,"fr_label":"Entrée libre","en_label":"Free"},"keywords":"","file":null,"icalendar_url":"https://memento.epfl.ch/event/export/120849/","category":{"id":1,"code":"CONF","fr_label":"Conférences - Séminaires","en_label":"Conferences - Seminars","activated":true},"academic_calendar_category":null,"domains":[],"mementos":["https://memento.epfl.ch/api/v1/mementos/7/?format=json","https://memento.epfl.ch/api/v1/mementos/427/?format=json"]},{"id":71943,"title":"NUMBER THEORY SEMINAR - Formalizing Jacobi's four-squares theorem in Lean 4","slug":"number-theory-seminar-formalizing-jacobi-s-four--2","event_url":"https://memento.epfl.ch/event/number-theory-seminar-formalizing-jacobi-s-four--2","visual_url":null,"visual_large_url":null,"visual_maxsize_url":null,"lang":"en","start_date":"2026-05-27","end_date":"2026-05-27","start_time":"15:00:00","end_time":"16:00:00","description":"Jacobi's theorem provides a closed formula for the number of representations of an integer as a sum of four squares, and can be proved as an introductory application of the theory of classic modular forms. In this talk, we outline its proof using Eisenstein and theta series. We then discuss the challenges of formalizing this proof in the Lean 4 proof assistant, using an algebraic strategy to derive the key dimension bound for the relevant space of modular forms from the valence formula for the full modular group.
","image_description":"","creation_date":"2026-05-26T14:26:39","last_modification_date":"2026-05-26T14:26:39","link_label":"","link_url":"","canceled":"True","cancel_reason":"","place_and_room":"GR A3 32","url_place_and_room":"https://plan.epfl.ch/?room==GR%20A3%2032","url_online_room":"","spoken_languages":["https://memento.epfl.ch/api/v1/spoken_languages/2/?format=json"],"speaker":"Tito Sacchi ","organizer":"","contact":"Laetitia Al-Sulaymaniyin","is_internal":"False","theme":"","vulgarization":{"id":2,"fr_label":"Public averti","en_label":"Informed public"},"registration":{"id":3,"fr_label":"Entrée libre","en_label":"Free"},"keywords":"","file":null,"icalendar_url":"https://memento.epfl.ch/event/export/120855/","category":{"id":1,"code":"CONF","fr_label":"Conférences - Séminaires","en_label":"Conferences - Seminars","activated":true},"academic_calendar_category":null,"domains":[],"mementos":["https://memento.epfl.ch/api/v1/mementos/5/?format=json","https://memento.epfl.ch/api/v1/mementos/7/?format=json"]},{"id":71946,"title":"Data-Driven Robust Controller Synthesis Framework using Non-Parametric Integral Quadratic Constraints","slug":"data-driven-robust-controller-synthesis-framewor-2","event_url":"https://memento.epfl.ch/event/data-driven-robust-controller-synthesis-framewor-2","visual_url":"https://memento.epfl.ch/image/33253/200x112.jpg","visual_large_url":"https://memento.epfl.ch/image/33253/720x405.jpg","visual_maxsize_url":"https://memento.epfl.ch/image/33253/max-size.jpg","lang":"en","start_date":"2026-06-12","end_date":"2026-06-12","start_time":"17:30:00","end_time":null,"description":"Thesis Director: Prof. A. Karimi,
\r\nRobotics, Control and Intelligent Systems doctoral program
\r\nThesis Nr. 11741
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\r\nTo take part in the public defense, please contact directly the speaker
The talk is jointly organized by the EPFL AI Center and the EPFL Machine Learning for Biomedicine Lab (MLBIO) as part of the AI Fundamentals seminar series.
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\r\nTitle
\r\nAgents That Know What They Know: Interpretability and Introspection for Lifelong Learning
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\r\nAbstract
\r\nOne of the hallmarks of intelligence is the ability to learn from experience. In artificial intelligence, we frame this as lifelong learning: autonomous agents that continue to adapt after deployment as they encounter new tasks and environments. In this talk, I will argue that successful lifelong learning agents require a form of introspection: they must be able to reason about the scope and limits of their own knowledge. This self-knowledge allows an agent to answer three fundamental questions. What do I know? When can I reuse what I know? And what do I still need to learn? I will present recent work from my group showing how ideas from interpretability and explainability can surface the knowledge needed to answer these questions. I will first show how learned representations can be used to identify when inputs are novel, enabling out-of-distribution detection. Then, I will discuss how this can be built upon to give agents a way to distinguish between situations where prior knowledge can be safely reused and situations where new learning is needed. Together, this work shows that interpretability is not only a tool for transparency, but a mechanism for building agents that recognize, reuse, and acquire knowledge over time.
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\r\nBio
\r\nJoseph Campbell is an Assistant Professor in the Department of Computer Science at Purdue University, where he leads the Collaborative AI for Machines and People Lab. His research bridges machine learning and robotics, with a focus on explainable machine learning and lifelong learning. Before joining Purdue, he was a Postdoctoral Fellow in the Robotics Institute at Carnegie Mellon University, and he received his Ph.D., M.S., and B.S. degrees from Arizona State University. His research is supported by Amazon, the Toyota Research Institute, and the National Science Foundation.
Thesis Director: Prof. Z. Patakfalvi,
\r\nMathematics doctoral program
\r\nThesis Nr. 12192
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\r\nTo take part in the public defense, please contact directly the speaker
Thesis Director: Prof. S. C. Olhede,
\r\nMathematics doctoral program
\r\nThesis Nr. 11276
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\r\nTo take part in the public defense, please contact directly the speaker