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        "event_title":"2026 Byrne Conference on Stochastic Analysis in Finance and Insurance",
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        "event_title":"Privacy for Structured Data Release: Time-Discounted Continual Release and Randomized Quantization",
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        "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 R\u00e9nyi 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.",
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        "event_title":"Combinatorial Optimization Problems Arising from Graph-Based Models",
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        "combined_title":"Combinatorial Optimization Problems Arising from Graph-Based Models: Samuel Boardman",
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        "event_title":"Dynamic Contracting: Sequential Payments, Stochastic Target Problems, and State-Constrained Control",
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        "description":"Abstract:\n\nThis thesis develops stochastic-control methods for dynamic principal\u2013agent problems in continuous time. The first part studies adverse selection with moral hazard, where the agent privately observes her type. We reformulate the principal\u2019s 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.",
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        "datetime_modified":"20260522T102454",
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        "event_title":"Learning with Quantum Examples: Multiclass, Online, and Smoothed Settings",
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        "combined_title":"Learning with Quantum Examples: Multiclass, Online, and Smoothed Settings: Preetham Mohan",
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        "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.",
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        "event_title":"Modular degree of elliptic curves over function fields in relation to Jacquet-Langlands",
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