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DTSTAMP:20250115T122544
DTSTART;TZID=America/Detroit:20250122T160000
DTEND;TZID=America/Detroit:20250122T170000
SUMMARY:Workshop / Seminar:Probability and Analysis Seminar: Toward a structure theory of disordered matrix product states
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 ‘‘efficient\,’’ the theory took root and is now an indispensable tool in many-body physics and quantum simulation. Recent work in this direction by Movassagh–Schenker (2022) and Nelson–R. (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 ‘‘one-way’’ construction\, not a classification. In this talk\, I’ll 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.
UID:131006-21867591@events.umich.edu
URL:https://events.umich.edu/event/131006
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3096
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20250120T212804
DTSTART;TZID=America/Detroit:20250122T160000
DTEND;TZID=America/Detroit:20250122T170000
SUMMARY:Lecture / Discussion:Student Model Theory Seminar
DESCRIPTION:First meeting of the student model theory reading seminar. Please contact Dhruv (dhruvkul@umich.edu) if you have any questions.
UID:131491-21868624@events.umich.edu
URL:https://events.umich.edu/event/131491
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Graduate Students,Mathematics,seminar,Talk,Undergraduate Students
LOCATION:East Hall - 1060
CONTACT:
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BEGIN:VEVENT
DTSTAMP:20250104T120928
DTSTART;TZID=America/Detroit:20250122T160000
DTEND;TZID=America/Detroit:20250122T170000
SUMMARY:Workshop / Seminar:Vector-valued robust stochastic control with applications to finance
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.
UID:129023-21862050@events.umich.edu
URL:https://events.umich.edu/event/129023
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1360
CONTACT:
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