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## Research Interests ##
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I design methods to **formally verify** that **algorithms** are correct. I am
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especially interested in programs satisfying quantitative guarantees, or
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especially interested in programs satisfying quantitative guarantees, or other
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properties from mathematical or scientific applications.
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A particular focus of my work has been verifying programs that use
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surprisingly challenging for computers to analyze. Drawing inspiration from how
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humans reason about randomized algorithms, we can build simpler and more
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automated verification techniques. In the past, I've applied this approach to
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properties like **accuracy**, **incentive compatibility**, Markov chain
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**mixing**, various notions of **algorithmic stability**, and [**differential
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privacy**](https://en.wikipedia.org/wiki/Differential_privacy), a rigorous
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definition of privacy. I have developed a variety of [**type
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systems**](https://en.wikipedia.org/wiki/Type_system) and [**program
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logics**](https://en.wikipedia.org/wiki/Hoare_logic) to verify that programs are
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differentially private.
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properties like **statistical accuracy**, **incentive compatibility**, Markov
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chain **mixing**, **algorithmic stability**, and **differential privacy**.
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More broadly, I am interested in verifying all kinds of programs and properties
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with rich mathematical structure, such as continuous-time systems, programs with
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symmetries, economic mechanisms, and most recently, algorithms from numerical
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More broadly, I am interested in verification for all kinds of programs with
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rich mathematical structure and properties, such as continuous-time systems,
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programs with symmetries, economic mechanisms, and algorithms from numerical
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analysis and applied mathematics.
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## Teaching ##
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