Posted January 15, 2025
Last modified January 21, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Saber Jafarpour, University of Colorado Boulder
Safety and Resilience of Learning-enabled Autonomous Systems: A Monotone Contracting System Perspective.
Abstract: Learning-enabled autonomous systems are increasingly deployed for decision-making in safety-critical environments. Despite their substantial computational advantages, ensuring the safety and reliability of these systems remains a significant challenge due to their high dimensionality and inherent nonlinearity. In this talk, we leverage tools and techniques from control theory to develop theoretical and algorithmic methods for certifying the safety and robustness of learning-enabled autonomous systems. Our approach investigates safety and resilience from a reachability perspective. We employ contraction and monotone systems theories to develop computationally efficient frameworks for approximating reachable sets of autonomous systems. We demonstrate how these frameworks can be applied to verify and train robust standalone neural networks and to provide run-time safety assurance in systems with learning-based controllers.
Posted December 5, 2024
Last modified January 22, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Ken Ono, University of Virginia
Partitions detect primes
This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Posted September 19, 2024
Last modified October 25, 2024
Colloquium Questions or comments?
3:30 pm Lockett 232
Bogdan Suceava, California State University Fullerton
TBD