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Challenging Computational Infeasibility: PCP and Boolean Functions
Challenging Computational Infeasibility: PCP and Boolean Functions
The field of Mathematics of Computation focuses on classifying algorithmic problems based on their computational time and memory requirements. Computer scientists have developed methodologies to assess whether specific algorithmic problems are solvable within given constraints. In cases where direct solutions are unattainable, researchers often devise approximation algorithms to find near-optimal solutions. The Unique-Games Conjecture, proposed two decades ago, serves as a tool for proving the infeasibility of approximation problems whose complexity remains unresolved. Our EU-funded PCPABF project builds upon our recent breakthrough paper, "Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion," which is recognized as a significant milestone towards resolving the Unique-Games Conjecture. Our aim is to complete the proof using innovative techniques. Importantly, these advancements have practical implications, particularly in addressing challenges related to pandemic spread, such as the COVID-19 crisis.
For more information, visit the project website.
This project is generously funded by the European Research Council. To learn more about the grant, click here.
Examining Our History Through the Lens of Ancient Sedimentary DNA
Examining Our History Through the Lens of Ancient Sedimentary DNA
Join our pioneering research project at the intersection of genetics and mathematics, where we're revolutionizing ancient DNA analysis by leveraging sediment samples. Our innovative approach integrates mathematical algorithms with expertise in aDNA data, ensuring a holistic understanding of our shared history. Led in conjunction by myself and paleogeneticist Dr. Viviane Slon, we're developing cutting-edge tools to comprehensively analyze sedimentary aDNA data. Through synergistic collaboration, we're crafting algorithms to co-analyze data across layers, maximizing likelihood scenarios to elucidate the history of ancient populations. Join us in reshaping genetic research and uncovering the past through a novel mathematical lens.
For more information, visit the project website.
This project is generously funded by the John F. Templeton Foundation. To learn more about the grant, click here.
The Mathematics of Lattices
The Mathematics of Lattices
Coming soon!
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