Ryan O'Donnell
Carnegie Mellon University, PA·Computer Science
Some mathematical networks link a huge number of points using surprisingly few connections, yet stay tightly interconnected. High-dimensional expanders (HDXs) are an advanced kind of such network.
- Fields
Computer Science
Mathematics & Statistics
- Topics
high-dimensional expanders
expander graphs
theoretical computer science
- Grants
- 1 known grant, through Jul 2029
What they work on
- Find new elementary methods for constructing high-dimensional expanders, highly interconnected mathematical networks, that avoid the advanced algebra and number theory used in current constructions.
- Determine which known HDX constructions have useful properties such as symmetry, constructivity and different kinds of local and global interconnectedness.
- Develop new applications of HDXs in coding theory, optimization and quantum computing, and explore possible uses in graph algorithms and data structures.
More about the research
They have recently driven breakthroughs in error-correcting codes (which protect data from errors), data-routing algorithms and quantum computing. Still, only a few ways to build HDXs are known, and those methods are hard to understand.
Why it matters
Simpler and better-understood high-dimensional expanders could give computer scientists new tools for error-correcting codes, optimization algorithms and quantum computing. These areas underpin reliable data storage and transmission and future quantum technologies. New teaching materials could also make this specialized topic easier for students to learn.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Paul Valiant
Purdue University, IN·Computer Science
Design error-correcting codes that withstand random or adversarial insertion and deletion errors while supporting local decoding, which recovers part of a message by reading only a small piece of the stored data.
Huy Pham
California Institute of Technology, CA·Mathematics & Statistics·Early-career
Develop new toolkits for first moment obstructions, where counting expected copies of a structure rules it out, to close gaps in the theory of threshold phenomena in random discrete systems.
Jean-Francois Biasse
University of South Florida, FL·Mathematics & Statistics
Investigate hard algebraic and number-theoretic problems, including finding short vectors in Euclidean lattices, isogenies between curves, and inverting group actions, as foundations for next-generation cryptosystems.
The school
Carnegie Mellon University: 28 labs on PI Pages, $505M a year on research, 346 research doctorates a year.
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