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Laura Monroe

Research scientist and project leader at Los Alamos National Laboratory

“Mathematical Aspects of Optically-Enabled Post-Exascale Systems”

Thursday 16 February, 8.30am – 9.05am


Recent advances in co-packaged optics make it possible to drive multiple terabytes per second out of a single socket. The photonic eco-system is advancing rapidly, making co-packaged optics an excellent candidate for upcoming generations of post-exascale systems, bringing speed-of-light latency for short- and long-reach communication, combined with an exponential growth of communication bandwidth and connectivity: it is now possible to drive 32-64 optical connections out of a single high-radix device.

This level of connectivity is a real advancement, but current network designs do not fully exploit this opportunity. Without advances in system design, these new systems will not reach their potential. Such advances are especially needed in network topology and system design, which are still open areas of research.

This talk is on the border of mathematics and computer science, working toward the design of such a topology. We will discuss the use of mathematical graph theory and projective geometry in the design of very large and compact interconnection networks that are optimally tailored to this emerging technology.

We have used classical graph theory and known graphs to create PolarFly, a new family of diameter-2 topologies. This topology supports radixes suited to the new high-radix routers, aymptotically approaches the maximum number of nodes for the radix and diameter, exploits mathematical symmetries for modularity, and outperforms other networks in terms of scalability, cost and performance.

Diameter 2 is suited to smaller systems, but not exascale. We will discuss current and future directions as well, aimed at exascale and post-exascale systems.


Dr. Laura Monroe is a research scientist and project leader at Los Alamos National Laboratory. She received her Ph.D. in Mathematics and Computer Science from the University of Illinois at Chicago, where she studied the theory of error-correcting codes. She worked at NASA Glenn following graduation, and joined LANL in 2000. Her interests are in the fields of discrete mathematics and computing, as well as in the mathematical bridge between the computer as physical object and as ideal system.

She now works at LANL’s Ultrascale Systems Research Center at the intersection of mathematics and computer science and in the field of novel computing, in particular probabilistic computing for high-performance applications. She was formerly the project leader for the laboratory’s Production Visualization project, where her last project was leading the build of LANL’s state-of-the-art visualization corridor, including large-scale visualization systems, large virtual reality theaters and networking and systems for desktop visualization.

She was named one of the seven 2019 NM Technology Council Women in Technology awardees. She has received several Defense Program Awards of Excellence and several LANL Distinguished Performance awards, both as team leader and team member, and received an R&D 100 award as part of the PixelVizion team. She has published in the fields of mathematics, network design, probabilistic computing, resilience, error-correcting codes, combinatorics and visualization.

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