On November 13, 2026, the University of Southern California announced a $6 million grant renewal from the Simons Foundation for an international research collaboration investigating the intersections of low-dimensional topology, quantum computing, and artificial intelligence. Directed by USC mathematician Aaron Lauda, the 11-institution initiative brings total foundation support to $14 million, providing multi-year stability for theoretical researchers while requiring sponsored research offices to manage complex cross-institutional subawards.
Expanding Low-Dimensional Topology and Quantum Braiding
The Simons Collaboration on New Structures in Low-Dimensional Topology was launched to unite pure mathematics with theoretical physics. Under the renewed three-year award detailed in the USC Dornsife announcement, USC will administer more than $2 million directly, distributing remaining funds across an international network of ten partner institutions, including Caltech, Stanford, Texas A&M, Columbia, Princeton, MIT, UCLA, and Harvard.
Low-dimensional topology investigates properties of knots, links, and three- and four-dimensional manifolds that remain unchanged under continuous deformation. In quantum physics, these topological features describe the worldlines of two-dimensional quasiparticles known as anyons. When anyons circulate around one another, their paths form mathematical braids. These braid structures provide an intrinsic shield against local thermal noise and decoherence, making topological systems a compelling architecture for fault-tolerant quantum computing.
A major hurdle in topological quantum computation has been that standard non-Abelian systems, such as Ising anyons, cannot execute universal quantum logic gates through braiding alone. In Nature Communications, collaboration director Aaron Lauda and co-investigators Filippo Iulianelli, Sung Kim, and Joshua Sussan resolved this limitation by introducing an expanded model with quasiparticles termed neglectons. By proving that neglectons enable universal quantum computation solely via topological braiding, the team demonstrated how knot algebra directly informs quantum hardware theory.
The exchange also flows in reverse. Collaboration researchers designed quantum algorithms capable of estimating Khovanov homology, an algebraic invariant used to distinguish knots. At USC, Associate Professor of Mathematics Cris Negron constructs algebraic frameworks linking representation theory, category theory, and quantum physics. Concurrently, Stanford researcher Qiuyu Ren and Texas A&M mathematician Michael Willis used knot invariants to distinguish smooth four-dimensional mathematical spaces, demonstrating how topological techniques advance across dimensions.
How Does Knot Mathematics Inform Quantum Error Correction and AI?
Knot mathematics informs quantum error correction by encoding logical quantum states into global topological configurations rather than fragile local states, while offering structured testbeds for training machine learning algorithms in sparse-reward environments. Because topological invariants depend solely on braid geometry rather than local perturbations, quantum gates mapped to knot structures resist environmental decoherence.
The collaboration applies these abstract structures to machine learning challenges. Caltech theoretical physicist Sergei Gukov and colleagues deployed reinforcement learning agents to investigate the Andrews-Curtis conjecture, a 60-year-old puzzle regarding whether complicated descriptions of the trivial group can always be simplified through fixed moves. In standard reinforcement learning, agents frequently fail when successful paths are extremely sparse. By pairing heuristic AI searches with rigorous algebraic reasoning, the team resolved several suspected counterexamples, establishing new methods for integrating AI into formal mathematical proof.
The grant also funds early-career mentorship. In Pasadena, California, the collaboration hosted a summer workshop at the American Institute of Mathematics, introducing graduate students and postdoctoral researchers to categorification, knot invariants, and quantum physics. This training pipeline equips emerging scholars with cross-disciplinary fluency across pure mathematics, computer science, and quantum theory.
Implications for Cross-Institutional Grants and Research Offices
The Simons Collaboration expansion illustrates key operational demands for university research offices administering multi-campus philanthropic awards. Distributing $6 million across 11 partner campuses requires sponsored programs administrators to negotiate complex subaward agreements between collaborating institutions. Research administrators must align institutional review processes, establish subrecipient monitoring schedules, and coordinate international researcher travel across partner campuses.
Sponsored project managers must also address differences between foundation policies and federal grant mechanisms. Institutional budget officers frequently evaluate foundation vs. federal indirect cost rates, as private funders like the Simons Foundation typically cap indirect cost recovery below standard negotiated federal rates. Host institutions must accommodate overhead adjustments while maintaining computing infrastructure, international conferences, and administrative management.
Additionally, theoretical collaborations producing software libraries, mathematical datasets, and preprints require governance across the grants management lifecycle. Ensuring compliance with open-science mandates, code reproducibility, and multi-author publication attribution is vital for post-award administration. Research offices increasingly deploy persistent grant DOI identifiers to track cross-institutional research outputs, facilitating transparent reporting back to private foundations.
Sources
- University of Southern California (USC Dornsife College of Letters, Arts and Sciences), “Knots, quantum computing and AI: $6m grant supports exploration of the surprising connections,” official announcement published November 13, 2026.
- Simons Foundation, “Simons Collaboration on New Structures in Low-Dimensional Topology,” collaborative award documentation and institutional roster, accessed November 2026.
