Modern cryptography must navigate the transition to post-quantum security while meeting the demands of real-world systems. Due to the tension between post-quantum security and performance, this transition entails complex challenges on several fronts. In this talk, I will discuss the intricacies of provable security and how to establish solid theory for cryptographic building blocks that underpin our digital society. First, I will briefly cover my past work on searchable encryption and zero-knowledge proofs. In the main part of the talk, I will highlight my research on tools for advanced authentication in a post-quantum world. In particular, I will present my recent works on threshold signatures and blind signatures and discuss how to achieve stronger security guarantees under weak assumptions. In the end, I will highlight some open problems that are urgent to solve.

AI systems increasingly reshape our networks, markets, and platforms. When deployed in social environments— online platforms, labor markets, and information ecosystems—AI interacts with complex human behavior, strategic incentives, and structural inequality. This talk focuses on foundational challenges and opportunities for AI systems: how to design and evaluate algorithmic interventions in complex social environments. I will present recent work on causal inference under competing treatments, which formalizes how competition for user attention and strategic behavior among experimenters distort experimental data and invalidate naïve estimates of algorithmic impact. By modeling experimentation as a strategic data acquisition problem, we show how evaluation itself becomes an optimization problem, and we derive mechanisms that recover meaningful estimates despite interference and competition. I connect this problem to deriving foundational properties of systems that enable reliable experimentation. Beyond this case study, the talk highlights broader implications for the design and evaluation of AI systems in networks, markets, and platforms. I argue that responsible deployment requires rethinking evaluation methodologies to account for incentives, feedback loops, and system-level effects, and I outline directions for how algorithmic and statistical tools can tackle these challenges.

AI is reshaping software development, yet this rapid adoption risks introducing a new generation of security debt. In this talk, I will present my research program aimed at transforming AI from a source of vulnerabilities to a security enabler. I will begin by introducing a systematic framework for quantifying AI-induced cybersecurity risks through two benchmarks: CyberGym, which evaluates AI agents’ offensive capabilities in vulnerability reproduction and discovery, and BaxBench, which measures LLMs’ propensity to introduce security flaws when generating code. Building on these findings, I will present a secure-by-design approach for AI-generated code. This includes security-centric fine-tuning that embeds secure coding practices directly into models, as well as a decoding-time constraining mechanism based on type systems to enforce safety guarantees. Finally, I will conclude by discussing my future research on building broader security and trust in AI-driven software ecosystems.

Algorithmic problems in infinite groups arise naturally in the analysis of computational models, and they forge a fundamental link between algebra, logic, and computation. The central aim of my research is to understand the boundary between decidability and undecidability in computational algebra and group theory. Despite significant advances in the past 80 years, essential questions on the nature of these boundaries remain largely unanswered. The decision problems that we consider (the Diophantine Problem, membership problems, intersection problems) are particularly relevant to algorithmic verification, automata theory, and program analysis. Our methodology relates algorithms in groups to other central problems in infinite state systems, first-order arithmetic theories, and computer algebra. In this talk, I will illustrate a few recent results that expand the known decidability frontier, as well as some immediate and impactful open problems.

Real-world AI systems must be robust across a wide range of conditions. One path to such robustness is if a model recovers a coherent structural understanding of its domain. But it is unclear how to measure, or even define, structural understanding. This talk will present theoretically-grounded definitions and metrics that test the structural recovery — or implicit "world models" — of generative models. We will propose different ways to formalize the concept of a world model, develop tests based on these notions, and apply them across domains. In applications ranging from testing whether LLMs apply logic to whether foundation models acquire Newtonian mechanics, we will see that models can make highly accurate predictions with incoherent world models. We will also connect these tests to a broader agenda of building generative models that are robust across downstream uses, incorporating ideas from statistics and the behavioral sciences. Developing reliable inferences about model behavior across tasks offer new ways to assess and improve the efficacy of generative models.

Machine learning (ML) and artificial intelligence (AI) are not standalone artifacts: they are ecosystems where foundation models are adapted and deployed through layered pipelines spanning developers, platforms, users and regulators. This talk explores how the structure of these ecosystems shapes the distribution of value and risk, and determines system-level properties like safety and fairness. I begin with a game-theoretic model of the interaction between general-purpose producers and domain specialists, using it to examine how regulatory design shapes incentives and equilibrium behaviors. I then connect these formal insights to empirical measurements from 1.86 million open-source AI models, reconstructing lineage networks to quantify how behaviors and failures propagate through fine-tuning. Finally, zooming in from the aggregate structure of the ecosystem to the design of the algorithms themselves, I describe my work in algorithmic fairness, framing the identification of less discriminatory algorithms as a search problem with provable statistical guarantees. I close by outlining a forward-looking research agenda aimed at building both the technical infrastructure and policy mechanisms required to steer AI ecosystems toward robust, accountable and democratic outcomes.

Floating-point numbers often represent real numbers in computer systems. They are applicable in many domains, including embedded systems, machine learning, and scientific computing. Despite their widespread use, they pose some difficulties. Floating-point numbers and operations typically suffer from roundoff errors, making computations over floating-points inaccurate with respect to a real-valued specification. Moreover, the IEEE 754 floating-point standard, a fundamental element in formalizing floating-point arithmetic for today’s computers, presents additional challenges due to special values and resulting unintuitive behaviors. This thesis has three main contributions that address existing gaps in automated reasoning about floating-point arithmetic, making it easier for developers and researchers to understand, verify, and trust the floating-point computations in their programs. First, we introduce the first floating-point support in a deductive verifier for the Java programming language. Our support in the KeY verifier automatically handles floating-point arithmetic and transcendental functions. We achieve this with a combination of delegation to external SMT solvers on one hand, and rule-based reasoning within KeY on the other, exploiting the complementary strengths of both approaches. As a result, this approach can prove functional floating-point properties for realistic programs. Second, inspired by KeY’s treatment of method calls and the need for a scalable roundoff error analysis, we present the first modular optimization-based roundoff error analysis for non-recursive procedural floating-point programs. Our key idea is to achieve modularity while maintaining reasonable accuracy by automatically computing procedure summaries that are a function of the input parameters. Technically, we extend an existing optimization-based roundoff error analysis and show how to effectively use first-order Taylor approximations to compute precise procedure summaries, and how to integrate those to obtain end-to-end roundoff error bounds. Third, our experience using SMT solvers to discharge KeY’s floating-point verification conditions revealed unexpected performance behavior, motivating a systematic study of floating-point reasoning in SMT solvers. We propose a metamorphic testing approach that uses semantics-preserving rewrite rules, focusing on floating-point special values, to uncover unexpected performance behavior in SMT solvers’ handling of floating-point formulas, such as an increase in solving time when the SMT queries are simplified. Using real-world test inputs, our approach can identify such performance bugs for every SMT solver tested.