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        "datetime_start":"20260116T143000",
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        "date_start":"2026-01-16",
        "date_end":"2026-01-16",
        "time_start":"14:30:00",
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        "time_zone":"America\/Detroit",
        "event_title":"Exterior Cyclic Polytopes and Convexity of Amplituhedra (Combinatorics Seminar)",
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        "combined_title":"Exterior Cyclic Polytopes and Convexity of Amplituhedra (Combinatorics Seminar): Lizzie Pratt (UC Berkeley)",
        "event_subtitle":"Lizzie Pratt (UC Berkeley)",
        "event_type":"Workshop \/ Seminar",
        "event_type_id":"21",
        "description":"We introduce a new polytope called the exterior cyclic polytope. Our motivation comes from particle physics, and in particular from a semialgebraic set called the amplituhedron which lives in a Grassmannian Gr(k, r) and appears in calculations of particle scattering. \r\n\r\nThe exterior cyclic polytope is defined as the convex hull of the amplituhedron in the ambient Pl\u00fccker space of Gr(k, r). We describe its face structure and facets, which in the case k=2 are controlled by a matroid called the hyperconnectivity matroid. Furthermore, we describe the dual of the k=2 and r=4 polytope in terms of the twist map of Marsh and Scott, and use this to define a notion of dual amplituhedron. This is joint work with Elia Mazzucchelli.",
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                "group_name":"Combinatorics Seminar - Department of Mathematics",
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    {
        "datetime_modified":"20251127T224606",
        "datetime_start":"20260116T150000",
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        "has_end_time":1,
        "date_start":"2026-01-16",
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        "time_zone":"America\/Detroit",
        "event_title":"AIM Seminar:  Metric lines in Carnot groups",
        "occurrence_title":"",
        "combined_title":"AIM Seminar:  Metric lines in Carnot groups: Alejandro Bravo-Doddoli (University of Michigan)",
        "event_subtitle":"Alejandro Bravo-Doddoli (University of Michigan)",
        "event_type":"Lecture \/ Discussion",
        "event_type_id":"13",
        "description":"Abstract:  Among nilpotent Lie groups, Carnot groups form a particularly important subclass, with the Heisenberg group being the most well-known example. Carnot groups admit a sub-Riemannian structure. Thus, to broaden the context, a sub-Riemannian geodesic is a local arc-length-minimizing curve. A natural question is: What are the conditions for a geodesic to be a global minimizer? A curve is called a metric line if it is a globally minimizing geodesic; an alternative term is \u201can isometric embedding of the real line.\u201d The talk is devoted to presenting the results and ideas that inspired me to formulate a conjecture classifying metric lines in Carnot groups, as well as the results obtained in this direction. \r\n\r\nContact:  AIM Seminar Organizers",
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                "guid":"141893-21889608@events.umich.edu",
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                "group_name":"Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics",
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