{ "143836-21894104": { "datetime_modified":"20260219T221509", "datetime_start":"20260225T160000", "datetime_end":"20260225T170000", "has_end_time":1, "date_start":"2026-02-25", "date_end":"2026-02-25", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Topology seminar: Top-dimensional cohomology of the congruence subgroup Gamma_{0,n}(p)", "occurrence_title":"", "combined_title":"Topology seminar: Top-dimensional cohomology of the congruence subgroup Gamma_{0,n}(p): Tatiana Abdelnaim", "event_subtitle":"Tatiana Abdelnaim", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Let Gamma_{0,n}(p) be the congruence subgroup of level p of SL_n(Z) whose first column is congruent to (*,0,\\dots,0)^t \\mod p. The cohomology of this subgroup has connections to problems in algebraic K-theory and number theory. Borel and Serre (1973) showed that the rational cohomology of Gamma_{0,n}(p) vanishes above degree n(n+1)\/2. \n\nWe prove that the top-dimensional rational cohomology group of Gamma_{0,n}(p) vanishes for all p equal to 2,3,5,7,13 and when n is at least 3, as well as for all primes p at most 6n-14. We also reprove the known non-vanishing result that this group is nonzero for n=2 for every prime p, and we establish a new non-vanishing for n=3 for all primes p not equal to 2,3,5,7,13. \n\nIn this talk, I will outline the ideas behind these results and briefly survey what is known about the top-dimensional cohomology of related congruence subgroups.", "occurrence_notes":null, "guid":"143836-21894104@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/143836", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3866", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"", "sponsors":[ { "group_name":"RTG Seminar on Geometry, Dynamics and Topology - Department of Mathematics", "group_id":"4900", "website":"" }, { "group_name":"Department of Mathematics", "group_id":"3791", "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":21894104 } , "143802-21894059": { "datetime_modified":"20260324T085405", "datetime_start":"20260225T160000", "datetime_end":"20260225T170000", "has_end_time":1, "date_start":"2026-02-25", "date_end":"2026-02-25", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Unpacking the News with U-M Faculty Experts", "occurrence_title":"", "combined_title":"Unpacking the News with U-M Faculty Experts: Join U-M Faculty experts to discuss what's happening now", "event_subtitle":"Join U-M Faculty experts to discuss what's happening now", "event_type":"Meeting", "event_type_id":"14", "description":"Each session offers a space to pause, sort out what\u2019s happening, and engage in thoughtful, civil discussion with peers. Bring your questions, your curiosity, and your perspective\u2014no preparation required.\n\nJosh Pasek is Professor of Communication & Media and Political Science, Faculty Associate at the Center for Political Studies, Institute for Social Research, and Associate Director of the Michigan Institute for Data Science at the University of Michigan.", "occurrence_notes":null, "guid":"143802-21894059@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/143802", "building_id":"1000191", "building_name":"Michigan League", "campus_maps_id":"108", "room":"Room 4", "location_name":"Michigan League", "has_livestream":0, "cost":"", "tags":["Civic Engagement","Civic Learning","Culture","Education","Free","In Person","Media","Politics","Social Impact","Talk","Undergraduate"], "website":"https:\/\/democracy.umich.edu\/", "sponsors":[ { "group_name":"Democracy & Civic Empowerment", "group_id":"5335", "website":"https:\/\/democracy.umich.edu\/" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/03\/event_143802_original-1.png", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/03\/event_143802_original-1.png", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2026\/03\/event_143802_original-1.png", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2026\/03\/event_143802_original-1.png", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2026\/03\/event_143802_original-1.png", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2026\/03\/event_143802_original-1.png", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2026\/03\/event_143802_original-1.png" }, "occurrence_count":13, "first_occurrence":21894053 } }