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Benedikt Bünz is an Assistant Professor of Computer Science at NYU Courant. He also cofounded and am the chief scientist of Espresso Systems. He researches applied cryptography, consensus and game theory, especially as it relates to cryptocurrencies. His...
Leo Orshansky is a PhD student at Columbia University since 2024, where he is currently pursuing research interests in the intersection of cryptography and quantum information. He is co-advised by Henry Yuen and Tal Malkin.
The classic theory of computing approach to designing and analyzing algorithms considers hand-designed algorithms and focuses on worst-case guarantees. Since such hand-designed algorithms have weak worst-case guarantees for many problems, in practice machine learning components are often incorporated in algorithm design. In this talk, I will describe recent work in our group that provides theoretical foundations for such learning augmented algorithms. I will describe both specific case studies (from data science to operations research to computational economics) and general principles applicable broadly to a variety of combinatorial algorithmic problems. I will then show how we can loop back and use these tools to learn machine learning algorithms themselves!
In 1966, Lennart Carleson published a proof of an important theorem in harmonic analysis, that states that the Fourier series converges pointwise to the original function under weak conditions. This result has a notoriously difficult proof, and while the result has been generalized, every found proof is full of intricate details. In my talk, I will describe an ongoing formalization project that verifies all the details of a generalized Carleson theorem in Lean. I will in particular reflect on the collaborative nature of this formalization.