{ "128978-21861970": { "datetime_modified":"20241109T195941", "datetime_start":"20241122T160000", "datetime_end":"20241122T170000", "has_end_time":1, "date_start":"2024-11-22", "date_end":"2024-11-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"GEOMETRY SEMINAR: Diophantine approximation on homogeneous spaces", "occurrence_title":"", "combined_title":"GEOMETRY SEMINAR: Diophantine approximation on homogeneous spaces: Amos Nevo (Chicago\/Technion)", "event_subtitle":"Amos Nevo (Chicago\/Technion)", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Let G be a Lie group, L a lattice in G, and H a closed subgroup of G.\r\nSuppose that L acts on the homogeneous space G\/H with dense orbits.\r\nWe would like to measure how dense these orbits actually are, or equivalently, gauge the efficiency of approximation of a general point on G\/H by a lattice orbit.\r\nDeparting from traditional classical Diophantine approximation, we will\r\nAssume G to be a non-amenable group, for example the group of isometries of hyperbolic space, or the general linear or affine group.\r\nWe will present a solution to this problem for lattice actions\r\non a large class of homogeneous spaces, emphasizing a sufficient condition for when an optimal result holds, and give some examples. The methods involve dynamical arguments, and spectral methods applied to the automorphic representation.\r\nWe will then briefly describe the extensive scope of this set-up, and explain some more refined problems related to equidistribution and discrepancy of lattice orbits, as time permits.\r\n\r\nBased partly on joint work with Alex Gorodnik and Anish Ghosh, and partly on recent joint work with Mikolaj Fraczyk and Alex Gorodnik.", "occurrence_notes":null, "guid":"128978-21861970@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/128978", "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":"Geometry Seminar - Department of Mathematics", "group_id":"4891", "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":21861970 } , "123530-21851037": { "datetime_modified":"20240723T152000", "datetime_start":"20241122T160000", "datetime_end":"20241122T170000", "has_end_time":1, "date_start":"2024-11-22", "date_end":"2024-11-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Guided Tour of the Clements Library", "occurrence_title":"", "combined_title":"Guided Tour of the Clements Library", "event_subtitle":"", "event_type":"Tours", "event_type_id":"25", "description":"Join us to learn more about the history of the Clements Library, its programs, and collections. Highlights include Benjamin West's iconic painting \"Death of General Wolfe,\" a Revolutionary War-era trunk that once housed General Thomas Gage's papers, and the current exhibit.\r\n\r\nArrive at our North Entrance to check-in for your tour. This entrance is accessible and an elevator is available to move between floors.\r\n\r\nWe want to ensure full participation in our events. If an accommodation would promote that, please let us know.", "occurrence_notes":null, "guid":"123530-21851037@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/123530", "building_id":"1000159", "building_name":"William Clements Library", "campus_maps_id":"165", "room":"", "location_name":"William Clements Library", "has_livestream":0, "cost":"", "tags":["american culture","american history","art history","Humanities","Library","Tour"], "website":"https:\/\/lp.constantcontactpages.com\/ev\/reg\/xrt3b79", "sponsors":[ { "group_name":"William L. Clements Library", "group_id":"1727", "website":"" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2024\/07\/event_123530_original-1.jpeg" }, "occurrence_count":1, "first_occurrence":21851037 } }