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After the collapse, an outgoing shock emerges and propagates outward.\n\nIn this talk, I will present our rigorous construction of self-similar converging and diverging shock solutions for the adiabatic exponent $\\gamma\\in(1,3]$. These solutions are analytic away from the shock interfaces and the blow-up point. The proof relies on continuity arguments, nonlinear invariances, and barrier functions.", "occurrence_notes":null, "guid":"138590-21883422@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/138590", "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":"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":21883422 } , "151708-21912005": { "datetime_modified":"20260908T120339", "datetime_start":"20261022T160000", "datetime_end":"20261022T170000", "has_end_time":1, "date_start":"2026-10-22", "date_end":"2026-10-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"EEB Thursday Seminar Series - The old field rules: the quest to develop generalizable principles about how ecosystems function", "occurrence_title":"", "combined_title":"EEB Thursday Seminar Series - The old field rules: the quest to develop generalizable principles about how ecosystems function: Oswald Schmitz, Yale University", "event_subtitle":"Oswald Schmitz, Yale University", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"Seminar Summary - The presentation will chronicle a journey of long-term research devoted to discovering fundamental principles\u2014rules of life\u2014that explain how animal species\u2019 adaptive evolutionary ecological interactions determine how they control ecosystem functioning. I will discuss how this research journey led to systematic resolution of generalizable principles that explain how ecosystems function. The fundamental lesson is that dedication to long-term theory-informed field research can lead to a coherent predictive understanding of how ecosystems function.", "occurrence_notes":null, "guid":"151708-21912005@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/151708", "building_id":"1005169", "building_name":"Biological Sciences Building", "campus_maps_id":"631", "room":"1060", "location_name":"Biological Sciences Building", "has_livestream":0, "cost":"", "tags":["Workshop","Talk","seminar","evolutionary biology","environmental","Environment","eeb","Ecosystems"], "website":"http:\/\/schmitz.environment.yale.edu\/os-schmitz.html", "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\/09\/event_151708_original-1.png", "styled_images":{ "event_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_thumb\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_large":"https:\/\/events.umich.edu\/media\/cache\/event_large\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_large_2x":"https:\/\/events.umich.edu\/media\/cache\/event_large_2x\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/event_large_lightbox\/media\/attachments\/2026\/09\/event_151708_original-1.png", "group_thumb":"https:\/\/events.umich.edu\/media\/cache\/group_thumb\/media\/attachments\/2026\/09\/event_151708_original-1.png", "group_thumb_square":"https:\/\/events.umich.edu\/media\/cache\/group_thumb_square\/media\/attachments\/2026\/09\/event_151708_original-1.png", "group_large":"https:\/\/events.umich.edu\/media\/cache\/group_large\/media\/attachments\/2026\/09\/event_151708_original-1.png", "group_large_lightbox":"https:\/\/events.umich.edu\/media\/cache\/group_large_lightbox\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_large_crop":"https:\/\/events.umich.edu\/media\/cache\/event_large_crop\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_list":"https:\/\/events.umich.edu\/media\/cache\/event_list\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_list_2x":"https:\/\/events.umich.edu\/media\/cache\/event_list_2x\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_grid":"https:\/\/events.umich.edu\/media\/cache\/event_grid\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_grid_2x":"https:\/\/events.umich.edu\/media\/cache\/event_grid_2x\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_feature_large":"https:\/\/events.umich.edu\/media\/cache\/event_feature_large\/media\/attachments\/2026\/09\/event_151708_original-1.png", "event_feature_thumb":"https:\/\/events.umich.edu\/media\/cache\/event_feature_thumb\/media\/attachments\/2026\/09\/event_151708_original-1.png" }, "occurrence_count":1, "first_occurrence":21912005 } }