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:20260404T131154Z UID:bM2L/1 DESCRIPTION:Title: Using machine learning to formulate mathematical conjectures\nby M arc Lackenby (University of Oxford) as part of Barcelona Mathematics and M achine Learning Colloquium Series\n\n\nAbstract\nI will describe how machi ne learning can be used as a tool for pure mathematicians to formulate new conjectures. I will initially focus on a discovery of a new connection be tween two different areas of low-dimensional topology and geometry. My col laborators and I were able to use fairly simple supervised learning to est ablish that the signature of a knot can be predicted from the knot's hyper bolic invariants. We were able to formulate this relationship as a precise conjecture\, that we eventually proved (in a slightly modified form). The method that we used is very general: it is likely to be applicable to man y area of mathematics. However\, in my talk\, I will discuss its limitatio ns\, which include the difficulty of interpreting the patterns that machin e learning discovers\, as well as the tendency for machine learning algori thms to ignore outliers. If there is time\, I will describe some new examp les where machine learning has been able to find unexpected conjectural co nnections in low-dimensional topology.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Elizabeth Munch (Michigan State University) DTSTART:20230315T140000Z DTEND:20230315T153000Z DTSTAMP:20260404T131154Z UID:bM2L/2 DESCRIPTION:Title: Crafting Topological Features for Machine Learning Pipelines\nby E lizabeth Munch (Michigan State University) as part of Barcelona Mathematic s and Machine Learning Colloquium Series\n\n\nAbstract\nThe field of topol ogical data analysis (TDA) has exploded in the last twenty years. This sui te of tools creates methods for quantifying shape in data by incorporating ideas from a wide range of subjects such as topology\, geometry\, algebra \, category theory\, and graph theory. In this talk we will discuss the ba sic setup of some of main tools in TDA\, how these can be fit into an ML p ipeline\, and show example applications highlighting the kinds of structur es that can be found with these methods.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jürgen Jost (Max Planck Institute\, Leipzig) DTSTART:20230426T130000Z DTEND:20230426T143000Z DTSTAMP:20260404T131154Z UID:bM2L/3 DESCRIPTION:Title: Generalized curvatures and the geometry of data\nby Jürgen Jost ( Max Planck Institute\, Leipzig) as part of Barcelona Mathematics and Machi ne Learning Colloquium Series\n\n\nAbstract\nCurvature is the most importa nt concept of Riemannian geometry\, and it has been extended to metric spa ces. Here\, I shall develop a notion of curvature that also applies to dis crete spaces (as occurring as data samples)\, links curvature to the conce pt of hyperconvexity and offers a geometric view on topological data analy sis.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Laurent Lafforgue (Huawei Research Centre France) DTSTART:20240208T130000Z DTEND:20240208T143000Z DTSTAMP:20260404T131154Z UID:bM2L/4 DESCRIPTION:Title: Some sketches for a topos-theoretic AI\nby Laurent Lafforgue (Huaw ei Research Centre France) as part of Barcelona Mathematics and Machine Le arning Colloquium Series\n\n\nAbstract\nThe purpose of this talk will be t o sketch a partial outline for building a new version of AI based on Groth endieck Topos Theory.\n\n We will first review some key facts which ma ke Grothendieck toposes a natural interface between logic and topology or geometry. We will explain in particular in which sense the semantics of an y first-order "geometric" theory can be incarnated by a topos\, so by a ma thematical object to which all intuitions of topological nature still appl y.\n\n Based on that\, we will consider anew the problem of designing good description languages for any type of real objects which we could wan t to represent mathematically\, with the aim of processing their represent ations. This would require the choice of a vocabulary. After such a descr iption vocabulary is chosen\, basic principles of Topos Theory yield a pro cess for deriving from instances of the type of real objects under conside ration some grammar rules relating the elements of vocabulary. These gram mar rules incarnate an interpretation principle for the type of objects un der consideration. The way they are derived using principles of Topos Theo ry can be considered as a modellization of inductive reasoning.\n\n Sup posing a good description language\, consisting in chosen elements of voca bulary and derived grammar rules\, has been elaborated\, the next and most difficult step would be to construct a topos-based process for extracting information. This would be a topos-theoretic version of Deep Learning. We will propose a general form for such topos-based processes and describe an induced framework which allows at least to think about this problem in a mathematical way.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Gitta Kutyniok (Ludwig-Maximilians-Universität München) DTSTART:20240311T130000Z DTEND:20240311T143000Z DTSTAMP:20260404T131154Z UID:bM2L/5 DESCRIPTION:Title: Reliability of Artificial Intelligence\, Chances and Challenges\nb y Gitta Kutyniok (Ludwig-Maximilians-Universität München) as part of Bar celona Mathematics and Machine Learning Colloquium Series\n\n\nAbstract\nA rtificial intelligence is currently leading to one breakthrough after the other\, both in public life with\, for instance\, autonomous driving and s peech recognition\, and in the sciences in areas such as medical imaging o r molecular dynamics. However\, one current major drawback worldwide\, in particular\, in light of regulations such as the EU AI Act and the G7 Hiro shima AI Process\, is the lack of reliability of such methodologies. \n\nI n this lecture\, we will provide an introduction into this vibrant researc h area\, focusing specifically on deep neural networks. We will discuss th e role of a theoretical perspective to this highly topical research direct ion\, and survey the current state of the art in areas such as explainabil ity. Finally\, we will also touch upon fundamental limitations of neural n etwork-based approaches.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Shing-Tung Yau (Tsinghua University\, Beijing) DTSTART:20240418T120000Z DTEND:20240418T133000Z DTSTAMP:20260404T131154Z UID:bM2L/6 DESCRIPTION:Title: Manifold Fitting: an Invitation to Machine Learning – a Mathematicia n’s view\nby Shing-Tung Yau (Tsinghua University\, Beijing) as part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n\nAbstr act\nNatural datasets have intrinsic patterns\, which can be summarized as the manifold distribution principle: the distribution of a class of data is close to a low-dimensional manifold. The manifold fitting problem can g o back to the solution to the Whitney extension problem leading to new ins ights for data interpolation. Assume that we are given a set $Y\\subseteq\ \mathbb{R}^D$. When can we construct a smooth d-dimensional submanifold $\ \widehat{M}\\subseteq\\mathbb{R}^D$ to approximate $Y$\, and how well can $\\widehat{M}$ estimate $Y$ in terms of distance and smoothness? However\, many of these methods rely on restrictive assumptions\, making extending them to efficient and workable algorithms challenging. As the manifold hyp othesis (non-Euclidean structure exploration) continues to be a foundation al element in data science\, the manifold fitting problem\, merits further exploration and discussion within the modern data science community. The talk will be partially based on some recent works [4\, 2\, 3\, 1] along wi th some on-going progress.\n\n[1] Zhigang Yao\, Bingjie Li\, Yukun Lu\, an d Shing-Tung Yau. Single-cell analysis via manifold fitting: A new framewo rk for RNA clustering and beyond\, 2024.\n\n[2] Zhigang Yao\, Jiaji Su\, B ingjie Li\, and Shing-Tung Yau. Manifold fitting. arXiv preprint 2304.0768 0\, 2023.\n\n[3] Zhigang Yao\, Jiaji Su\, and Shing-Tung Yau. Manifold fit ting with cycleGAN. Proceedings of the National Academy of Sciences of the United States of America\, 121(5):e2311436121\, 2023.\n\n[4] Zhigang Yao and Yuqing Xia. Manifold fitting under unbounded noise. arXiv preprint 190 9.10228\, 2019.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Fefferman (Princeton University) DTSTART:20250206T140000Z DTEND:20250206T153000Z DTSTAMP:20260404T131154Z UID:bM2L/7 DESCRIPTION:Title: Personal encounters with machine learning (postponed)\nby Charles Fefferman (Princeton University) as part of Barcelona Mathematics and Mach ine Learning Colloquium Series\n\nAbstract: TBA\n\nThis talk has been post poned. You can sign up to receive information about it once it is reschedu led.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Kristin Lauter (FAIR at META) DTSTART:20250327T160000Z DTEND:20250327T170000Z DTSTAMP:20260404T131154Z UID:bM2L/8 DESCRIPTION:Title: Artificial Intelligence & Cryptography: Privacy and Security in the AI era\nby Kristin Lauter (FAIR at META) as part of Barcelona Mathematic s and Machine Learning Colloquium Series\n\n\nAbstract\nHow is Artificial Intelligence 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 predict outcomes with high assurance. Such predictions can be used to make decisions automatically or give recommendations with high confidence . Cryptography is the science of protecting the privacy and security of da ta. This talk will explain the dynamic relationship between cryptography a nd AI and how AI can be used to attack post-quantum cryptosystems.\n LOCATION:https://stable.researchseminars.org/talk/bM2L/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Geordie Williamson DTSTART:20250508T070000Z DTEND:20250508T083000Z DTSTAMP:20260404T131154Z UID:bM2L/9 DESCRIPTION:Title: Searching for interesting mathematical objects with neural networks\nby Geordie Williamson as part of Barcelona Mathematics and Machine Lear ning Colloquium Series\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/bM2L/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Adi Shamir DTSTART:20260216T130000Z DTEND:20260216T143000Z DTSTAMP:20260404T131154Z UID:bM2L/10 DESCRIPTION:Title: Deep Neural Cryptography\nby Adi Shamir as part of Barcelona Math ematics and Machine Learning Colloquium Series\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/bM2L/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Carlos Simpson DTSTART:20260312T130000Z DTEND:20260312T143000Z DTSTAMP:20260404T131154Z UID:bM2L/11 DESCRIPTION:Title: Reinforcement learning for proofs\nby Carlos Simpson as part of B arcelona Mathematics and Machine Learning Colloquium Series\n\nAbstract: T BA\n LOCATION:https://stable.researchseminars.org/talk/bM2L/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Charles Fefferman DTSTART:20260427T130000Z DTEND:20260427T143000Z DTSTAMP:20260404T131154Z UID:bM2L/12 DESCRIPTION:Title: Personal encounters with machine learning\nby Charles Fefferman a s part of Barcelona Mathematics and Machine Learning Colloquium Series\n\n Abstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/bM2L/12/ END:VEVENT END:VCALENDAR