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In this talk, we focus on many-body quantum systems with Coulomb interactions, which play a central role in electronic and molecular dynamics. We prove that first-order Trotterization for such unbounded Hamiltonians admits a polynomial dependence on the number of particles in the continuum limit, with a convergence rate of order $1\/4$\u2014in contrast to prior Trotter analyses for bounded operators, which diverge in this limit. The result holds for all initial wavefunctions in the domain of the Hamiltonian. This $1\/4$-order rate is optimal, as previous work shows that it can be saturated by the ground state of the hydrogen atom. Moreover, higher-order Trotter formulas do not improve the worst-case scaling. We also discuss additional regularity conditions on the initial state under which the original Trotter convergence rate can be recovered. Finally, we discuss our recent development on the spatial error and algorithm complexities.", "occurrence_notes":null, "guid":"149190-21905948@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/149190", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"4088", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics","Quantum","Applied Mathematics"], "website":"", "sponsors":[ { "group_name":"Differential Equations Seminar - Department of Mathematics", "group_id":"4888", "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":21905948 } , "150132-21908116": { "datetime_modified":"20260811T130726", "datetime_start":"20260910T160000", "datetime_end":"20260910T170000", "has_end_time":1, "date_start":"2026-09-10", "date_end":"2026-09-10", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"EEB Thursday Seminar Series - Patterns of Growth and Mortality in an Endangered Cactus", "occurrence_title":"", "combined_title":"EEB Thursday Seminar Series - Patterns of Growth and Mortality in an Endangered Cactus: Amy Boyd, Warren Wilson College", "event_subtitle":"Amy Boyd, Warren Wilson College", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Studying the biology of endangered plants can provide insights into what these species need to thrive, especially in the face of climate change and other human impacts. This talk will focus on more than 30 years of study of an endangered cactus, Echinocactus horizonthalonius var. nicholii, as my colleagues and I have worked to understand the biology, ecology, and threats to this little-known species. I'll also talk about the value and challenge of long-term ecological research and my experience teaching at a small liberal arts college.", "occurrence_notes":null, "guid":"150132-21908116@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/150132", "building_id":"1005169", "building_name":"Biological Sciences Building", "campus_maps_id":"631", "room":"1060", "location_name":"Biological Sciences Building", "has_livestream":0, "cost":"", "tags":["Ecology","Workshop","Ecology & Biology","Ecology And Evolutionary Biology","ecosystem","Ecosystems","eeb","Environment","environmental","evolution","evolutionary biology","seminar","Talk"], "website":"", "sponsors":[ { "group_name":"Ecology and Evolutionary Biology", "group_id":"1190", "website":"" }, { "group_name":"EEB Thursday Seminars", "group_id":"3822", "website":"" } ], "image_url":"https:\/\/events.umich.edu\/media\/attachments\/2026\/08\/event_150132_original-1.png", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/08\/event_150132_original-1.png", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2026\/08\/event_150132_original-1.png", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2026\/08\/event_150132_original-1.png", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2026\/08\/event_150132_original-1.png", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2026\/08\/event_150132_original-1.png", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2026\/08\/event_150132_original-1.png" }, "occurrence_count":1, "first_occurrence":21908116 } }