{ "131006-21867591": { "datetime_modified":"20250115T122544", "datetime_start":"20250122T160000", "datetime_end":"20250122T170000", "has_end_time":1, "date_start":"2025-01-22", "date_end":"2025-01-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Probability and Analysis Seminar: Toward a structure theory of disordered matrix product states", "occurrence_title":"", "combined_title":"Probability and Analysis Seminar: Toward a structure theory of disordered matrix product states: Eric Roon (Michigan State University)", "event_subtitle":"Eric Roon (Michigan State University)", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"In 1992, Fannes, Nachtergaele, and Werner classified translation invariant states on quantum spin chains and discovered that they admit a matrix product structure. Such matrix product states are simultaneously good approximations for general states, and natural candidates for ground states of specific local Hamiltonians. Following the observation by Vidal (2004) that matrix product states are \u2018\u2018efficient,\u2019\u2019 the theory took root and is now an indispensable tool in many-body physics and quantum simulation. Recent work in this direction by Movassagh\u2013Schenker (2022) and Nelson\u2013R. (2024) adapted this structure to states generated by disordered matrix products. All such disordered matrix product states are translation co-variant. However both works above only had a \u2018\u2018one-way\u2019\u2019 construction, not a classification. In this talk, I\u2019ll report on some work in progress with Jeffrey Schenker where we successfully classify the translation co-variant states when the underlying probability space is a compact Hausdorff space.", "occurrence_notes":null, "guid":"131006-21867591@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/131006", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3096", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"https:\/\/sites.google.com\/view\/probsemumich\/future-talks", "sponsors":[ { "group_name":"Probability and Analysis Seminar - Department of Mathematics", "group_id":"5203", "website":"https:\/\/sites.google.com\/view\/probsemumich\/future-talks" }, { "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":21867591 } , "131491-21868624": { "datetime_modified":"20250120T212804", "datetime_start":"20250122T160000", "datetime_end":"20250122T170000", "has_end_time":1, "date_start":"2025-01-22", "date_end":"2025-01-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Student Model Theory Seminar", "occurrence_title":"", "combined_title":"Student Model Theory Seminar: Ilir Ziba", "event_subtitle":"Ilir Ziba", "event_type":"Lecture \/ Discussion", "event_type_id":"13", "description":"First meeting of the student model theory reading seminar. Please contact Dhruv (dhruvkul@umich.edu) if you have any questions.", "occurrence_notes":null, "guid":"131491-21868624@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/131491", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"1060", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Graduate Students","Mathematics","seminar","Talk","Undergraduate Students"], "website":"", "sponsors":[ { "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":21868624 } , "129023-21862050": { "datetime_modified":"20250104T120928", "datetime_start":"20250122T160000", "datetime_end":"20250122T170000", "has_end_time":1, "date_start":"2025-01-22", "date_end":"2025-01-22", "time_start":"16:00:00", "time_end":"17:00:00", "time_zone":"America\/Detroit", "event_title":"Vector-valued robust stochastic control with applications to finance", "occurrence_title":"", "combined_title":"Vector-valued robust stochastic control with applications to finance: Igor Cialenco\/IIT", "event_subtitle":"Igor Cialenco\/IIT", "event_type":"Workshop \/ Seminar", "event_type_id":"21", "description":"We study a dynamic stochastic control problem subject to Knightian uncertainty with multi-objective (vector-valued) criteria. Assuming the preferences across expected multi-loss vectors are represented by a given, yet general, preorder, we address the model uncertainty by adopting a robust or minimax perspective, minimizing expected loss across the worst-case model. In contrast to the scalar case, major challenges for multi-loss control problems include properly defining and interpreting the notions of supremum and infimum, and addressing the non-uniqueness of these suprema and infima. To deal with these, we employ the notion of an ideal point vector-valued supremum for the robust part of the problem, while we view the control part as a multi-objective (or vector) optimization problem. Using a set-valued framework, we derive both a weak and strong version of the dynamic programming principle (DPP) or Bellman equations by taking the value function as the collection of all worst expected losses across all feasible actions. The weak version of Bellman's principle is proved under minimal assumptions. To establish a stronger version of DPP, we introduce the rectangularity property with respect to a general preorder. We also further study a particular, but important, case of component-wise partial order of vectors, for which we additionally derive DPP under a different set-valued notion for the value function, the so-called upper image of the multi-objective problem. Finally, we provide illustrative examples motivated by financial problems.", "occurrence_notes":null, "guid":"129023-21862050@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/129023", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"1360", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"", "sponsors":[ { "group_name":"Financial\/Actuarial Mathematics Seminar - Department of Mathematics", "group_id":"4890", "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":21862050 } }