{
    "147638-21901454":
    {
        "datetime_modified":"20260410T162654",
        "datetime_start":"20260423T100000",
        "datetime_end":"20260423T120000",
        "has_end_time":1,
        "date_start":"2026-04-23",
        "date_end":"2026-04-23",
        "time_start":"10:00:00",
        "time_end":"12:00:00",
        "time_zone":"America\/Detroit",
        "event_title":"A Novel Construction for $\\mathfrak{sl}_4$ Webs",
        "occurrence_title":"",
        "combined_title":"A Novel Construction for $\\mathfrak{sl}_4$ Webs: Diya Yang",
        "event_subtitle":"Diya Yang",
        "event_type":"Presentation",
        "event_type_id":"16",
        "description":"Abstract: The standard monomial basis for $\\mathfrak{sl}_r$-invariant polynomials is indexed by rectangular standard Young tableaux, but it lacks rotational invariance. Although promotion induces a cyclic action on tableaux, a more symmetric basis is desirable. For $\\mathfrak{sl}_2$ and $\\mathfrak{sl}_3$, such bases are given by non-crossing matchings and non-elliptic $\\mathfrak{sl}_3$ webs, respectively. In the case of $\\mathfrak{sl}_4$, a web basis has recently been constructed using hourglass plabic graphs, but this approach relies on intricate growth rules and does not readily generalize to higher rank.\n\nIn this thesis, we introduce a simpler and more direct construction of $\\mathfrak{sl}_4$ webs. Starting from a rectangular four-row standard Young tableau, we construct the associated web by stacking the $\\mathfrak{sl}_3$ webs corresponding to the top three rows and the bottom three rows, identifying along the non-crossing matching determined by the middle two rows. We prove that the resulting web is fully reduced and lies in the same equivalence class as the $\\mathfrak{sl}_4$ web obtained via growth rules.",
        "occurrence_notes":null,
                "guid":"147638-21901454@events.umich.edu",
        "permalink":"http:\/\/events.umich.edu\/event\/147638",
        "building_id":"1000166",
        "building_name":"East Hall",
        "campus_maps_id":"53",
        "room":"3096",
        "location_name":"East Hall",
        "has_livestream":0,
        "cost":"",
        "tags":["Dissertation","Graduate","Graduate Students","Mathematics"],
        "website":"",
        "sponsors":[
             {
                "group_name":"Dissertation Defense - Department of Mathematics",
                "group_id":"4889",
                "website":""                }                    ],
        "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
        "styled_images":{
                                        "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_thumb\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_thumb_square\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "group_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/resolve\/group_large_lightbox\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_large_crop\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_list":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_list\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_grid_2x\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_large\/media\/attachments\/2026\/04\/event_147638_original-1.jpg",
                                            "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/resolve\/event_feature_thumb\/media\/attachments\/2026\/04\/event_147638_original-1.jpg"                    },
        "occurrence_count":1,
        "first_occurrence":21901454
    }    }