BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Marc Lackenby (University of Oxford) DTSTART:20230222T140000Z DTEND:20230222T153000Z DTSTAMP:20260314T080352Z UID:bM2L/1 DESCRIPTION:Title: Usi ng machine learning to formulate mathematical conjectures\nby Marc Lac kenby (University of Oxford) as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nI will describe how machine lear ning can be used as a tool for pure mathematicians to formulate new conjec tures. I will initially focus on a discovery of a new connection between t wo different areas of low-dimensional topology and geometry. My collaborat ors and I were able to use fairly simple supervised learning to establish that the signature of a knot can be predicted from the knot's hyperbolic i nvariants. We were able to formulate this relationship as a precise conjec ture\, that we eventually proved (in a slightly modified form). The method that we used is very general: it is likely to be applicable to many area of mathematics. However\, in my talk\, I will discuss its limitations\, wh ich include the difficulty of interpreting the patterns that machine learn ing discovers\, as well as the tendency for machine learning algorithms to ignore outliers. If there is time\, I will describe some new examples whe re machine learning has been able to find unexpected conjectural connectio ns in low-dimensional topology.\n LOCATION:https://researchseminars.org/talk/bM2L/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Elizabeth Munch (Michigan State University) DTSTART:20230315T140000Z DTEND:20230315T153000Z DTSTAMP:20260314T080352Z UID:bM2L/2 DESCRIPTION:Title: Cra fting Topological Features for Machine Learning Pipelines\nby Elizabet h Munch (Michigan State University) as part of Barcelona Mathematics and M achine Learning Colloquium Series\n\n\nAbstract\nThe field of topological data analysis (TDA) has exploded in the last twenty years. This suite of t ools creates methods for quantifying shape in data by incorporating ideas from a wide range of subjects such as topology\, geometry\, algebra\, cate gory theory\, and graph theory. In this talk we will discuss the basic set up of some of main tools in TDA\, how these can be fit into an ML pipeline \, and show example applications highlighting the kinds of structures that can be found with these methods.\n LOCATION:https://researchseminars.org/talk/bM2L/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürgen Jost (Max Planck Institute\, Leipzig) DTSTART:20230426T130000Z DTEND:20230426T143000Z DTSTAMP:20260314T080352Z UID:bM2L/3 DESCRIPTION:Title: Gen eralized curvatures and the geometry of data\nby Jürgen Jost (Max Pla nck Institute\, Leipzig) as part of Barcelona Mathematics and Machine Lear ning Colloquium Series\n\n\nAbstract\nCurvature is the most important conc ept of Riemannian geometry\, and it has been extended to metric spaces. He re\, I shall develop a notion of curvature that also applies to discrete s paces (as occurring as data samples)\, links curvature to the concept of h yperconvexity and offers a geometric view on topological data analysis.\n LOCATION:https://researchseminars.org/talk/bM2L/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Lafforgue (Huawei Research Centre France) DTSTART:20240208T130000Z DTEND:20240208T143000Z DTSTAMP:20260314T080352Z UID:bM2L/4 DESCRIPTION:Title: Som e sketches for a topos-theoretic AI\nby Laurent Lafforgue (Huawei Rese arch Centre France) as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nThe purpose of this talk will be to sketc h a partial outline for building a new version of AI based on Grothendieck Topos Theory.\n\n We will first review some key facts which make Grot hendieck toposes a natural interface between logic and topology or geometr y. We will explain in particular in which sense the semantics of any first -order "geometric" theory can be incarnated by a topos\, so by a mathemati cal object to which all intuitions of topological nature still apply.\n\n Based on that\, we will consider anew the problem of designing good de scription languages for any type of real objects which we could want to re present mathematically\, with the aim of processing their representations. This would require the choice of a vocabulary. After such a description vocabulary is chosen\, basic principles of Topos Theory yield a process fo r deriving from instances of the type of real objects under consideration some grammar rules relating the elements of vocabulary. These grammar rul es incarnate an interpretation principle for the type of objects under con sideration. The way they are derived using principles of Topos Theory can be considered as a modellization of inductive reasoning.\n\n Supposing a good description language\, consisting in chosen elements of vocabulary and derived grammar rules\, has been elaborated\, the next and most diffic ult step would be to construct a topos-based process for extracting inform ation. This would be a topos-theoretic version of Deep Learning. We will p ropose a general form for such topos-based processes and describe an indu ced framework which allows at least to think about this problem in a mathe matical way.\n LOCATION:https://researchseminars.org/talk/bM2L/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gitta Kutyniok (Ludwig-Maximilians-Universität München) DTSTART:20240311T130000Z DTEND:20240311T143000Z DTSTAMP:20260314T080352Z UID:bM2L/5 DESCRIPTION:Title: Rel iability of Artificial Intelligence\, Chances and Challenges\nby Gitta Kutyniok (Ludwig-Maximilians-Universität München) as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nArtifici al intelligence is currently leading to one breakthrough after the other\, both in public life with\, for instance\, autonomous driving and speech r ecognition\, and in the sciences in areas such as medical imaging or molec ular dynamics. However\, one current major drawback worldwide\, in particu lar\, in light of regulations such as the EU AI Act and the G7 Hiroshima A I Process\, is the lack of reliability of such methodologies. \n\nIn this lecture\, we will provide an introduction into this vibrant research area\ , focusing specifically on deep neural networks. We will discuss the role of a theoretical perspective to this highly topical research direction\, a nd survey the current state of the art in areas such as explainability. Fi nally\, we will also touch upon fundamental limitations of neural network- based approaches.\n LOCATION:https://researchseminars.org/talk/bM2L/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shing-Tung Yau (Tsinghua University\, Beijing) DTSTART:20240418T120000Z DTEND:20240418T133000Z DTSTAMP:20260314T080352Z UID:bM2L/6 DESCRIPTION:Title: Man ifold Fitting: an Invitation to Machine Learning – a Mathematician’s v iew\nby Shing-Tung Yau (Tsinghua University\, Beijing) as part of Barc elona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nNa tural datasets have intrinsic patterns\, which can be summarized as the ma nifold distribution principle: the distribution of a class of data is clos e to a low-dimensional manifold. The manifold fitting problem can go back to the solution to the Whitney extension problem leading to new insights f or data interpolation. Assume that we are given a set $Y\\subseteq\\mathbb {R}^D$. When can we construct a smooth d-dimensional submanifold $\\wideha t{M}\\subseteq\\mathbb{R}^D$ to approximate $Y$\, and how well can $\\wide hat{M}$ estimate $Y$ in terms of distance and smoothness? However\, many o f these methods rely on restrictive assumptions\, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational elem ent in data science\, the manifold fitting problem\, merits further explor ation and discussion within the modern data science community. The talk wi ll be partially based on some recent works [4\, 2\, 3\, 1] along with some on-going progress.\n\n[1] Zhigang Yao\, Bingjie Li\, Yukun Lu\, and Shing -Tung Yau. Single-cell analysis via manifold fitting: A new framework for RNA clustering and beyond\, 2024.\n\n[2] Zhigang Yao\, Jiaji Su\, Bingjie Li\, and Shing-Tung Yau. Manifold fitting. arXiv preprint 2304.07680\, 202 3.\n\n[3] Zhigang Yao\, Jiaji Su\, and Shing-Tung Yau. Manifold fitting wi th cycleGAN. Proceedings of the National Academy of Sciences of the United States of America\, 121(5):e2311436121\, 2023.\n\n[4] Zhigang Yao and Yuq ing Xia. Manifold fitting under unbounded noise. arXiv preprint 1909.10228 \, 2019.\n LOCATION:https://researchseminars.org/talk/bM2L/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Fefferman (Princeton University) DTSTART:20250206T140000Z DTEND:20250206T153000Z DTSTAMP:20260314T080352Z UID:bM2L/7 DESCRIPTION:Title: Per sonal encounters with machine learning (postponed)\nby Charles Fefferm an (Princeton University) as part of Barcelona Mathematics and Machine Lea rning Colloquium Series\n\nAbstract: TBA\n\nThis talk has been postponed. You can sign up to receive information about it once it is rescheduled.\n LOCATION:https://researchseminars.org/talk/bM2L/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristin Lauter (FAIR at META) DTSTART:20250327T160000Z DTEND:20250327T170000Z DTSTAMP:20260314T080352Z UID:bM2L/8 DESCRIPTION:Title: Art ificial Intelligence & Cryptography: Privacy and Security in the AI era\nby Kristin Lauter (FAIR at META) as part of Barcelona Mathematics and M achine Learning Colloquium Series\n\n\nAbstract\nHow is Artificial Intelli gence changing your life and the world? How do you expect your data to be kept secure and private in the future? Artificial intelligence (AI) refers to the science of utilizing data to formulate mathematical models that pr edict outcomes with high assurance. Such predictions can be used to make d ecisions automatically or give recommendations with high confidence. Crypt ography is the science of protecting the privacy and security of data. Thi s talk will explain the dynamic relationship between cryptography and AI a nd how AI can be used to attack post-quantum cryptosystems.\n LOCATION:https://researchseminars.org/talk/bM2L/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Geordie Williamson DTSTART:20250508T070000Z DTEND:20250508T083000Z DTSTAMP:20260314T080352Z UID:bM2L/9 DESCRIPTION:Title: Sea rching for interesting mathematical objects with neural networks\nby G eordie Williamson as part of Barcelona Mathematics and Machine Learning Co lloquium Series\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/bM2L/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Adi Shamir DTSTART:20260216T130000Z DTEND:20260216T143000Z DTSTAMP:20260314T080352Z UID:bM2L/10 DESCRIPTION:Title: De ep Neural Cryptography\nby Adi Shamir as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/bM2L/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Simpson DTSTART:20260312T130000Z DTEND:20260312T143000Z DTSTAMP:20260314T080352Z UID:bM2L/11 DESCRIPTION:Title: Re inforcement learning for proofs\nby Carlos Simpson as part of Barcelon a Mathematics and Machine Learning Colloquium Series\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/bM2L/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Fefferman DTSTART:20260427T130000Z DTEND:20260427T143000Z DTSTAMP:20260314T080352Z UID:bM2L/12 DESCRIPTION:Title: Pe rsonal encounters with machine learning\nby Charles Fefferman as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\nAbstrac t: TBA\n LOCATION:https://researchseminars.org/talk/bM2L/12/ END:VEVENT END:VCALENDAR