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"description":"I will discuss the combinatorial construction of the moduli space of stable tropical curves with labeled marked points, as a generalized simplicial complex parametrizing marked weighted metric graphs, with special attention to the representations of the symmetric group in its rational homology, with the action induced by permuting the marked points. In genus 0 and 1, these representations grow factorially in the number of marked points, but carry a \"secret filtration\" whose graded pieces are representation stable.\r\n\r\nAlthough I will present the complex in question as a moduli space for tropical curves, it has other natural interpretations, e.g. as topological quotients of Culler-Vogtmann Outer Space, Harvey's complex of curves on a punctured surface, and Hatcher's complex of sphere systems; and as the dual complex of the boundary divisor in the Deligne-Mumford moduli space of stable algebraic curves. Hence the properties of this space and its homology have interpretations in each of these contexts.\r\n\r\nBased on joint work with Melody Chan and Soren Galatius. Speaker(s): Sam Payne (Yale U.)", "occurrence_notes":null, "guid":"33267-4712525@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/33267", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"4088", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"", "sponsors":[ { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" }, { "group_name":"Combinatorics Seminar - Department of Mathematics", "group_id":"4885", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":4712525 } }