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CIS Seminar: “Efficient Probabilistically Checkable Proofs from High-Dimensional Expanders”

February 18, 2025 at 3:30 PM - 4:30 PM

The PCP theorem, proved in the 90’s, shows how to encode a proof for any theorem into a format where the theorem’s correctness can be verified by making only a constant number of queries to the proof. This result is a significant milestone in computer science and has important implications for approximation algorithms, cryptography, and cloud computing.

In this talk, I will cover some exciting progress on constructing efficient PCPs. My work gives a systematic way to construct PCPs, improving upon the state-of-the-art PCP constructions from nearly 20 years ago. This implies that many well-known approximation algorithms are nearly-optimal under well-believed complexity-theoretic conjectures. In the process, we also solve various conjectures in property testing and distributed computing. These advances are facilitated by the newly-emerging theory of high-dimensional expansion and draw upon connections with various areas of theoretical computer science and mathematics.

Mitali Bafna

Mathematics, MIT

 Mitali Bafna is a postdoc at MIT who is broadly interested in theoretical computer science. She was a postdoc at CMU from 2022-2023 and she graduated from Harvard in 2022 advised by Prof. Madhu Sudan. Her research focuses on complexity theory and algorithms, specifically the complexity of combinatorial optimization problems, high-dimensional expanders and sum of squares algorithms.

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Venue

  • Amy Gutmann Hall, Room 414
  • 3333 Chestnut Street
    Philadelphia, 19104 United States     + Google Map