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BEGIN:VEVENT
DTSTAMP:20260521T091353
DTSTART;TZID=America/Detroit:20260603T100000
DTEND;TZID=America/Detroit:20260603T120000
SUMMARY:Presentation:Privacy for Structured Data Release: Time-Discounted Continual Release and Randomized Quantization
DESCRIPTION:Abstract:\n\nDifferential privacy provides a formal framework for limiting disclosure risk in computations on sensitive data. This dissertation studies differential privacy in structured data-release settings\, focusing on two forms of structure: temporal structure in continual release and quantization structure in finite-level release.\n\nFirst\, we propose time-discounted differential privacy (TDDP) for continual release. Standard continual-release privacy definitions do not distinguish events by temporal distance\, whereas the time-discounted formulation allows privacy requirements to decay as events become older. We develop mechanisms for this setting and analyze their privacy and utility guarantees.\n\nSecond\, we analyze the Random Quantization Mechanism (RQM) of Youn et al.\, a mechanism that provides privacy-preserving randomized quantization through subsampling. The mechanism itself is not a contribution of this thesis\; rather\, we derive\, under specified hyperparameter calibration requirements\, a formal privacy characterization of RQM\, including Rényi DP guarantees\, a max-divergence/pure-DP refinement\, and reconstruction-error bounds. These results make precise privacy claims that were not explicitly established in the original presentation of the mechanism. We then study RQM as a randomized quantization procedure\, focusing on how preprocessing choices affect its behavior on unbounded and heavy-tailed data.\n\nFinally\, we complement the theoretical analysis with an empirical study of RQM in several new settings\, beginning with private mean estimation and then considering distributional approximation\, clustering\, and image obfuscation. The results show that RQM is most natural when quantization is already compatible with the intended data representation\, while also highlighting its sensitivity to parameter choices and application context.
UID:148370-21904025@events.umich.edu
URL:https://events.umich.edu/event/148370
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Graduate,Graduate Students,Mathematics
LOCATION:East Hall - 4088
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260515T084125
DTSTART;TZID=America/Detroit:20260603T110000
DTEND;TZID=America/Detroit:20260603T130000
SUMMARY:Presentation:Structural Effects in Network Dynamical Systems: From Reconstruction to Pattern Formation in Hypergraphs
DESCRIPTION:Abstract:\n\nThis dissertation studies how interaction structure influences the behavior of network dynamical systems and\, more fundamentally\, which aspects of that structure are dynamically observable. While complex systems are often modeled through underlying interaction networks or hypergraphs\, the relationship between structure and dynamics is not direct: different analytical frameworks reveal different structural projections.\n\nFirst\, we study the inverse problem of reconstructing higher-order interaction structure from pairwise observations. We show that such reconstruction is fundamentally non-unique\, establishing intrinsic limitations on structural inference from graph data.\n\nNext\, we analyze network dynamical systems on graphs and show that\, in the linear regime\, structural effects are mediated through coupling operators and their associated spectral and degree-based representations. We further identify intrinsic obstructions to coupling-induced stabilization.\n\nFinally\, extending these ideas to reaction–diffusion systems on directed hypergraphs\, we develop a weakly nonlinear reduction framework for pattern formation near bifurcation. We show that the resulting nonlinear dynamics depend not on the full higher-order interaction structure\, but on specific projected quantities\, termed packing contributions\, which govern pattern selection and saturation. This leads to a characterization of the notion of dynamical graph surrogacy\, under which higher-order interactions become dynamically indistinguishable from pairwise ones.\n\nTaken together\, these results show that structural effects are fundamentally analysis-dependent and provide a unified perspective on the limits of structural inference and the role of higher-order interactions in complex dynamical systems.
UID:148299-21903824@events.umich.edu
URL:https://events.umich.edu/event/148299
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Graduate,Graduate Students,Mathematics,Dissertation
LOCATION:East Hall - 3088
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260522T140614
DTSTART;TZID=America/Detroit:20260604T140000
DTEND;TZID=America/Detroit:20260604T160000
SUMMARY:Presentation:Combinatorial Optimization Problems Arising from Graph-Based Models
DESCRIPTION:Abstract:\n\nWe propose and analyze several graph-defined combinatorial optimization problems inspired by multiple application areas.  \n\nFirst\, we consider an influence maximization model that uses the independent cascade approach\, but allows two types for packets of information\, +1 and -1. These represent the change in a receiver's sentiments on a product or belief on an empirical question (regarded as their \"bias\")\, which can be justified via Bayes' rule. The algorithmic problems we study may be viewed as taking a more fine-grained approach to traditional influence maximization problems\, and correspondingly exhibit non-trivial behavior even in the unbudgeted version where packets are unlimited—including tractability that depends on the probability parameters of the independent cascade dynamics. On the other hand\, we obtain NP-hardness results for the budgeted version more analogous to previous work. Several natural heuristics are shown to induce substantial reductions of bias in simulations with well-known social network datasets.  \n\nNext\, given an undirected graph representing similarities between a set of items and an additive measure evaluating them\, we treat the position of a special subset of items in an ordinal ranking through a collection of problems in which items may be combined if they are similar. The objective for these problems is to either maximize or minimize the absolute or relative rank of the special subset\, with a meta-goal of assessing the robustness of the rank\, even in the presence of a well-defined criterion. We classify the computational complexity of all four problems\, mostly finding worst-case hardness\, then find exact and approximate solutions to special cases and variants of the problems. These structured cases are inspired by numerous real-world examples and may be used to assess commonly cited facts across disparate domains\, as we demonstrate for sources of greenhouse gas emissions that contribute to climate change. We then adapt our framework to require subsets of comparable measure\, converting the above ranking problems into redistricting problems\, with analogues to the former's grid variants. Emphasis is placed on worst-case deviations from proportional representation and an urban-rural model in which gerrymandering ability is curtailed.
UID:148410-21904197@events.umich.edu
URL:https://events.umich.edu/event/148410
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Graduate,Graduate Students,Mathematics
LOCATION:East Hall - 4088
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260521T115745
DTSTART;TZID=America/Detroit:20260605T120000
DTEND;TZID=America/Detroit:20260605T140000
SUMMARY:Presentation:Dynamic Contracting: Sequential Payments\, Stochastic Target Problems\, and State-Constrained Control
DESCRIPTION:Abstract:\n\nThis thesis develops stochastic-control methods for dynamic principal–agent problems in continuous time. The first part studies adverse selection with moral hazard\, where the agent privately observes her type. We reformulate the principal’s problem as an optimal control problem with partial information and state constraints\, and characterize the value through state-constrained HJB equations. The second part studies sequential contracting with multiple lump-sum payments at fixed dates\, using recursive BSDEs to reduce the Stackelberg problem to a single stochastic control problem with mixed static and continuous controls. The third part allows the principal to choose both the timing and size of discretionary bonuses\, leading to a mixed control-stopping problem characterized by HJB variational inequalities. Together\, the thesis shows how private information\, payment timing\, and contractual flexibility shape optimal incentive design.
UID:148372-21904151@events.umich.edu
URL:https://events.umich.edu/event/148372
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics,Graduate Students,Graduate,Dissertation
LOCATION:East Hall - 4096
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260522T102454
DTSTART;TZID=America/Detroit:20260605T130000
DTEND;TZID=America/Detroit:20260605T150000
SUMMARY:Presentation:Learning with Quantum Examples: Multiclass\, Online\, and Smoothed Settings
DESCRIPTION:Abstract:\n\nAs quantum computing progresses toward fault-tolerant architectures\, the question of which computational tasks admit provable quantum advantages and which do not has become increasingly central. Learning theory\, and in particular learning from quantum examples\, provides one of the few settings in which unconditional quantum-classical separations can be established. In distribution-free (i.e.\, worst-case) PAC learning\, existing results show that quantum examples provide no asymptotic advantage in sample complexity. In contrast\, under the uniform distribution\, unbounded quantum-classical separations are known for learning Fourier-sparse Boolean functions. Together\, these results reveal a striking dichotomy. However\, this understanding has largely been developed in the context of learning Boolean functions in the batch setting\, leaving open how these phenomena extend more broadly. This thesis develops the theory of learning with quantum examples beyond the batch Boolean setting along three directions: multiclass learning\, online learning\, and smoothed learning.\n\nIn the multiclass PAC setting\, we establish upper and lower bounds on quantum sample complexity in both the realizable and agnostic regimes\, finding that quantum examples continue to yield no distribution-independent separation from classical examples\, with learning rates governed by the Natarajan dimension up to logarithmic factors in the label-space size. We next study online learning\, where no standard framework for learning with quantum examples existed prior to this work. We provide such a model by lifting the classical online framework to one in which the adversary provides distributions over labeled examples\, and then by encoding these distributions as quantum examples. We establish expected regret guarantees for binary and multiclass classification in both the realizable and agnostic settings. The central finding is that unrestricted adversarial power permits highly concentrated distributions that dequantize the learning problem. Motivated by this dequantization phenomenon\, we develop a smoothed learning framework that constrains distributions to be smooth\, interpolating between the concentrated-distribution regime\, in which no quantum advantage exists\, and the uniform-distribution regime\, in which unbounded separations are known. For the class of Fourier-sparse Boolean functions\, we show that such separations persist throughout a nontrivial near-uniform regime in both the batch and online settings.\n\nTogether\, these results paint a coherent picture of learning with quantum examples beyond the batch Boolean setting\, showing that quantum-classical separations depend on the interplay between hypothesis class structure\, distributional assumptions\, and the degree of adversarial control permitted in the learning process.
UID:148398-21904185@events.umich.edu
URL:https://events.umich.edu/event/148398
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Mathematics,Graduate Students,Graduate
LOCATION:East Hall - 3088
CONTACT:
END:VEVENT
BEGIN:VEVENT
DTSTAMP:20260527T111038
DTSTART;TZID=America/Detroit:20260609T110000
DTEND;TZID=America/Detroit:20260609T130000
SUMMARY:Presentation:Modular degree of elliptic curves over function fields in relation to Jacquet-Langlands
DESCRIPTION:Abstract:\n\nIn this thesis\, we study the geometry of automorphic forms in the function field setting. The primary goal of this thesis prove a formula relating degrees of modular parametrization of an elliptic curve by different Drinfeld modular curves. This is analogous to the similar result of Ribet-\nTakahashi [RT97] in the number field setting\, which relates degrees of modular parameterizations of an elliptic curve over Q by varying Shimura curves. To prove this result\, I prove a result analogous to Ribet’s short exact sequence [Rib90a] which relates the special fibers of Shimura varieties at different primes. Using this technical result I deduce (in the function field case) level-lowering results akin to those of Ribet [Rib90a] and relations between Petersson inner products of modular forms that are related by the Jacquet-Langlands correspondence similar to the work of K. Prasanna [Pra03].
UID:148433-21904254@events.umich.edu
URL:https://events.umich.edu/event/148433
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation,Graduate,Graduate Students,Mathematics
LOCATION:Off Campus Location
CONTACT:
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