{
  "schema": "complex-trees/talks/1",
  "updated": "2026-09-24",
  "url": "https://complextrees.com/talks/",
  "description": "Recordings, slides and teaching materials by Bernat Espigulé: complex trees, self-similar sets, connectedness loci and mathematical visualization.",
  "author": {
    "name": "Bernat Espigulé",
    "url": "https://complextrees.com/"
  },
  "channel": {
    "name": "Bernat Espigulé",
    "url": "https://www.youtube.com/@bernatree",
    "id": "UCUSba82Z5jiC-kN7nE2-BnQ"
  },
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      "id": "owns-2026",
      "title": "Restricted polynomial roots, reciprocal power series, and finite capture for collinear affine IFS",
      "date": "2026-06-16",
      "year": 2026,
      "date_label": "16 June",
      "venue": "One World Numeration Seminar · Online",
      "description": "Restricted polynomial roots, reciprocal power series and finite capture in the connectedness loci of collinear affine iterated function systems. Based on joint work with David Juher, building on earlier work with David Juher and Joan Saldaña.",
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          "primary": true
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        {
          "url": "https://researchseminars.org/talk/OWNS/168/",
          "label": "Seminar & abstract"
        },
        {
          "url": "https://arxiv.org/abs/2603.07397",
          "label": "Related preprint"
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      ],
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        {
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        },
        {
          "url": "https://www.irif.fr/~numeration/uploads/Main/espigule_20260616.pdf",
          "primary": true,
          "note": "79-page public presentation hosted by the seminar. Title, speaker, collaborators and 16 June 2026 date verified against the cover; PDF size 16,810,091 bytes. Checked 24 September 2026."
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      ],
      "keywords": [
        "OWNS",
        "numeration",
        "finite capture",
        "restricted polynomials"
      ],
      "slides": 79
    },
    {
      "id": "bojos-2026",
      "title": "Arbres complexos i conjunts auto-similars",
      "date": "2026-04-25",
      "year": 2026,
      "date_label": "25 April",
      "venue": "Bojos per la Ciència i les Matemàtiques · Universitat de Barcelona",
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      "slides": 206,
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          "note": "The title slide gives the title, venue and 25 April 2026 event date."
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      ]
    },
    {
      "id": "ihp-2026",
      "title": "Finite capture and the closure of roots of restricted polynomials",
      "date": "2026-03-27",
      "year": 2026,
      "date_label": "27 March",
      "venue": "Integrating Research and Illustration in Number Theory · Institut Henri Poincaré, Amphithéâtre Hermite",
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      "note": "Recording published 19 May 2026.",
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      "title": "Collinear Fractals & Bandt’s Conjecture: Hidden Geometry of Polynomial Roots",
      "date": "2025-08-14",
      "year": 2025,
      "date_label": "14 August",
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      "note": "Recording published 30 September 2025. Programme title: “Parameter Space Level Sets of n-ary Collinear Fractals: From Polynomial Roots to Mandelbrot-like Loci Mn”.",
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      "title": "Beyond Roots of Integer Polynomials: The Connectivity of Collinear Fractals",
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      "sort_date": "2025-03-19",
      "date_label": "March · PDF export",
      "venue": "Presentation materials",
      "description": "Integer polynomial roots and the connectedness of collinear fractals; joint work with Joan Saldaña and David Juher.",
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    {
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      "title": "Asymptotic self-similarity between collinear fractals E(c,2n-1) and the Mandelbrot set ℳn for E(c,n)",
      "date": "2024-12-16",
      "year": 2024,
      "date_label": "Published 16 December",
      "venue": "Mathematical animation · Bernat Espigulé’s YouTube channel",
      "description": "A short animation linking collinear fractals and their parameter space.",
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          "primary": true
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        {
          "url": "https://doi.org/10.3390/fractalfract8120725",
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          "duration_seconds": 49
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    {
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      "title": "Mandelbrot set ℳn for collinear fractals E(c,n)",
      "date": "2024-06-10",
      "year": 2024,
      "date_label": "10 June",
      "venue": "International Online GSDUAB Seminar · Universitat Autònoma de Barcelona",
      "description": "Connectedness loci, self-affine tiles and zeros of power series with integer coefficients; joint work with David Juher and Joan Saldaña.",
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      ],
      "note": "Programme title: “Mandelbrot set ℳn associated to self-affine tiles and zeros of power series with integer coefficients.” The recording and slides preserve the June 2024 presentation; see the published paper for the subsequent results and their precise hypotheses.",
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          "note": "Official seminar archive documents the date, programme title, collaborators and direct recording link."
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        {
          "url": "https://complextrees.com/collinear/talks/Talk2024June10th.pdf",
          "primary": true,
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      "slides": 54
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    {
      "id": "cornell-2022",
      "title": "Families of Connected Self-similar Sets",
      "date": "2022-06-07",
      "year": 2022,
      "date_label": "7 June",
      "venue": "7th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals · Cornell University, Malott Hall 251",
      "description": "An introductory course on families of connected self-similar sets.",
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          "url": "https://www.youtube.com/watch?v=lpy3-VloR7s",
          "label": "Watch recording · 34:31",
          "primary": true
        },
        {
          "url": "https://math.cornell.edu/7th-cornell-conference-analysis-probability-and-mathematical-physics-fractals",
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      ],
      "note": "Recording published 22 June 2022.",
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          "primary": true,
          "note": "Public uploader description and player metadata"
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          "note": "Official conference page linked by the author"
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      ],
      "language": "English"
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    {
      "id": "wolfram-history-2021",
      "title": "History of Mathematics Project: Learning Journeys for Kids and Others",
      "date": "2021",
      "year": 2021,
      "date_label": "Event year",
      "venue": "Wolfram Technology Conference 2021",
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    {
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      "title": "Structural Stability of Connected Self-similar Sets",
      "date": "2021-04-09",
      "year": 2021,
      "date_label": "9 April",
      "venue": "Workshop on Topological and Combinatorial Dynamics · Centre de Recerca Matemàtica · Online",
      "description": "Complex trees and connected self-similar sets.",
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      "title": "Arbres fractals",
      "date": "2021-01-27",
      "year": 2021,
      "date_label": "27 January",
      "venue": "Arbres complexos i conjunts autosimilars · Museu de Matemàtiques de Catalunya (MMACA) · Online",
      "description": "Una conferència divulgativa sobre arbres fractals, amb imatges de la seva generació i transformació.",
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      "title": "Complex Trees: Structural Stability of Connected Self-Similar Sets",
      "date": "2019-12-08",
      "year": 2019,
      "date_label": "8 December",
      "venue": "2019 CMS Winter Meeting · Toronto, Ontario",
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        },
        {
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        }
      ],
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    {
      "id": "icerm-november-2019",
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      ],
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      "links": [
        {
          "url": "/talks/slides/icerm-november-2019/",
          "label": "Read recovered slides",
          "primary": true
        }
      ],
      "note": "Static recovery of the original Keynote export. Animations, embedded video and incremental builds are not reproduced. “Complex Trees” is the catalogue title; the cover identifies the speaker, event and date.",
      "sources": [
        {
          "url": "https://complextrees.com/talks/slides/icerm-november-2019/slides.json",
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          "note": "Recovered presentation metadata records the original order, cover information, source commit and file checksums.",
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      ],
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        {
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      ],
      "note": "Recording published 12 November 2019. Seminar title: “Complex Trees: Structural Stability of Connected Self-similar Sets”. Static recovery of the original Keynote export. Animations, embedded video and incremental builds are not reproduced.",
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          "primary": true,
          "note": "Public uploader description and player metadata"
        },
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        {
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      "archived": true,
      "links": [
        {
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          "label": "Read recovered slides",
          "primary": true
        }
      ],
      "note": "Static recovery of the original Keynote export. Animations, embedded video and incremental builds are not reproduced.",
      "sources": [
        {
          "url": "https://complextrees.com/talks/slides/icerm-unfolding-2019/slides.json",
          "primary": true,
          "note": "Recovered presentation metadata records the original order, cover information, source commit and file checksums.",
          "source_commit_sha": "46ae86a389fba74285410a9e217272fbe2976752"
        }
      ],
      "keywords": [
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        "unfolding",
        "rotational symmetry",
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    },
    {
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        }
      ],
      "note": "Animation; date refers to the video’s publication.",
      "sources": [
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      ],
      "video_metadata": [
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      "formats": [
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      ],
      "archived": true,
      "links": [
        {
          "url": "/talks/slides/bridges-2019/",
          "label": "Read recovered slides",
          "primary": true
        },
        {
          "url": "https://archive.bridgesmathart.org/2019/bridges2019-147.html",
          "label": "Related paper"
        }
      ],
      "note": "Static recovery of the original Keynote export. Animations, embedded video and incremental builds are not reproduced. The event month is documented; no day is assigned.",
      "sources": [
        {
          "url": "https://complextrees.com/talks/slides/bridges-2019/slides.json",
          "primary": true,
          "note": "Recovered presentation metadata records the original order, cover information, source commit and file checksums.",
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      ],
      "keywords": [
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    {
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      "year": 2019,
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      "formats": [
        "slides"
      ],
      "archived": true,
      "links": [
        {
          "url": "/talks/slides/topics-2019/",
          "label": "Read recovered slides",
          "primary": true
        },
        {
          "url": "https://www.gsd.uab.cat/tcd2019/index.php?id=talks",
          "label": "Conference programme"
        },
        {
          "url": "https://arxiv.org/abs/1902.11282",
          "label": "Related preprint"
        }
      ],
      "note": "Static recovery of the original Keynote export. Animations, embedded video and incremental builds are not reproduced. Programme title: “Complex trees and their families of connected self-similar sets”.",
      "sources": [
        {
          "url": "https://complextrees.com/talks/slides/topics-2019/slides.json",
          "primary": true,
          "note": "Recovered presentation metadata records the original order, cover date, source commit and file checksums.",
          "source_commit_sha": "8dba2ac146bd3ed7b6562733e91bf5eed4596d41"
        },
        {
          "url": "https://www.gsd.uab.cat/tcd2019/index.php?id=talks",
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          "note": "Official conference listing verifies speaker and programme title."
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      ],
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    },
    {
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      "formats": [
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      ],
      "archived": true,
      "links": [
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          "url": "https://complextrees.com/CT2018_Sept/",
          "label": "Open Keynote presentation",
          "primary": true
        },
        {
          "url": "https://hdl.handle.net/2445/129385",
          "label": "Master’s thesis"
        }
      ],
      "note": "The title slide dates the presentation to 16 July 2018; the original September-labelled URL is preserved.",
      "sources": [
        {
          "url": "https://complextrees.com/CT2018_Sept/",
          "note": "Public first-slide accessibility text gives 16 July 2018, Complex Trees, and the Holomorphic Dynamics Group."
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      ]
    },
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        "material"
      ],
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      "links": [
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          "primary": true
        },
        {
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        },
        {
          "url": "https://www.wolfram.com/events/technology-conference/2016/presentations/",
          "label": "Conference programme"
        }
      ],
      "sources": [
        {
          "url": "https://www.wolfram.com/events/technology-conference/2016/presentations/",
          "note": "Wolfram conference programme identifies the speaker, presentation and event."
        },
        {
          "url": "https://www.wolfram.com/broadcast/video.php?v=1698",
          "note": "Public provider record identifies the recording and its publication metadata."
        }
      ],
      "video_metadata": [
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          "provider_id": "191974954",
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          "uploaded_at": "2016-11-17 10:00:55",
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          "url": "https://www.wolfram.com/broadcast/video.php?v=1698"
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      ],
      "note": "Recording uploaded 17 November 2016."
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    {
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      "language": "English",
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          "primary": true
        },
        {
          "url": "https://www.wolfram.com/events/technology-conference/2015/presentations/",
          "label": "Conference programme"
        }
      ],
      "sources": [
        {
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          "note": "Wolfram conference programme identifies the speaker, presentation and event."
        },
        {
          "url": "https://www.youtube.com/watch?v=G6VPK9aIB_o",
          "note": "Public provider record identifies the recording and its publication metadata."
        }
      ],
      "video_metadata": [
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      ],
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        {
          "url": "https://www.youtube.com/watch?v=GgIJVq2QPiE",
          "label": "Watch recording · 13:01",
          "primary": true
        },
        {
          "url": "https://www.wolfram.com/broadcast/video.php?v=1404",
          "label": "Wolfram archive"
        }
      ],
      "note": "Conference year shown. Vimeo upload: 13 July 2015; YouTube upload: 30 December 2015.",
      "sources": [
        {
          "url": "https://www.youtube.com/watch?v=GgIJVq2QPiE",
          "primary": true,
          "note": "Public uploader description and player metadata"
        },
        {
          "url": "https://www.wolfram.com/broadcast/video.php?v=1404",
          "primary": true,
          "note": "Wolfram archive embeds Vimeo 133371503"
        },
        {
          "url": "https://vimeo.com/api/oembed.json?url=https://vimeo.com/133371503",
          "primary": true,
          "note": "Provider metadata labels the event 2015 EWTC and gives duration 781 seconds"
        }
      ],
      "video_metadata": [
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          "provider_id": "GgIJVq2QPiE",
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        }
      ],
      "language": "English",
      "sort_date": "2015-07-13"
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    {
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      "date": "2014",
      "year": 2014,
      "date_label": "Event year",
      "venue": "European Wolfram Technology Conference 2014",
      "description": "Wolfram Language experiments connecting Raspberry Pi with the physical world.",
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      "language": "English",
      "links": [
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          "label": "Watch recording · 13:14",
          "primary": true
        },
        {
          "url": "https://www.wolfram.com/broadcast/video.php?c=368&disp=list&v=1103",
          "label": "Conference programme"
        }
      ],
      "sources": [
        {
          "url": "https://www.wolfram.com/broadcast/video.php?c=368&disp=list&v=1103",
          "note": "Wolfram conference programme identifies the speaker, presentation and event."
        },
        {
          "url": "https://vimeo.com/api/oembed.json?url=https://vimeo.com/99176299",
          "note": "Provider metadata identifies the European Wolfram Technology Conference 2014 and a 25 June 2014 upload."
        }
      ],
      "note": "Conference year shown; the recording was uploaded on 25 June 2014.",
      "sort_date": "2014-06-25",
      "video_metadata": [
        {
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          "url": "https://www.wolfram.com/broadcast/video.php?v=1086",
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          "duration_seconds": 794
        }
      ]
    },
    {
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      "year": 2014,
      "date_label": "Published 20 February",
      "venue": "Research presentation video · Bernat Espigulé’s YouTube channel",
      "description": "A research presentation video about self-contacting symmetric fractal trees.",
      "formats": [
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      ],
      "links": [
        {
          "url": "https://www.youtube.com/watch?v=x-XCaQRroIg",
          "label": "Watch presentation video · 14:59",
          "primary": true
        }
      ],
      "note": "Video publication date shown. The author’s description connects this work with the 2014 Joint Mathematics Meetings art exhibition.",
      "sources": [
        {
          "url": "https://www.youtube.com/watch?v=x-XCaQRroIg",
          "primary": true,
          "note": "Public uploader description and player metadata"
        },
        {
          "url": "http://gallery.bridgesmathart.org/exhibitions/2014-joint-mathematics-meetings/geonat",
          "primary": true,
          "note": "Art exhibition linked in the author description"
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      ],
      "video_metadata": [
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          "provider_id": "x-XCaQRroIg",
          "own_channel": true,
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}