Po-Shen Loh is a professor at Carnegie Mellon University and a coach for the US Math Olympiad. He is also a social entrepreneur where he has his used his passion and expertise in mathematics in the service of education (expii.com) and epidemiology (novid.org). In this podcast, we discuss the mathematics behind Loh’s novel approach to contact tracing in the fight against COVID. Originally published on March 3, 2022 on Youtube: https://youtu.be/8CLxLBMGxLE Timestamps: 00:00:00 : Introduction 00:01:11 : About Po-Shen Loh 00:03:49 : NOVID app 00:04:47 : Graph theory and quarantining 00:08:39 : Graph adjacency definition for contact tracing 00:16:01 : Six degrees of separation away from anyone? 00:21:13 : Getting the game theory and incentives right 00:30:40 : Conventional approach to contact tracing 00:34:47 : Comparison with big tech 00:39:19 : Neighbor search complexity 00:45:15 : Watts-Strogatz small networks phenomenon 00:48:37 : Storing neighborhood information 00:57:00 : Random hashing to reduce computational burden 01:05:24 : Logarithmic probing of sparsity 01:09:56 : Two math PhDs struggle to do division 01:11:17 : Bitwise-or for union of bounded sets 01:16:21 : Step back and recap 01:26:15 : Tradeoff between number of hash bins and sparsity 01:29:12 : Conclusion Further reading: Po-Shen Loh. ”Flipping the Perspective in Contact Tracing” https://arxiv.org/abs/2010.03806 Originally published on March 3, 2022 on Youtube: https://youtu.be/8CLxLBMGxLE Timestamps: 00:00:00 : Introduction. 00:01:11 : About Po-Shen Loh 00:03:49 : NOVID app 00:04:47 : Graph theory and quarantining. 00:08:39 : Graph adjacency definition for contact tracing 00:16:01 : Six degrees of separation away from anyone? 00:21:13 : Getting the game theory and incentives right 00:30:40 : Conventional approach to contact tracing 00:34:47 : Comparison with big tech 00:39:19 : Neighbor search complexity 00:45:15 : Watts-Strogatz small networks phenomenon 00:48:37 : Storing neighborhood information 00:57:00 : Random hashing to reduce computational burden 01:05:24 : Logarithmic probing of sparsity 01:09:56 : Two math PhDs struggle to do division 01:11:17 : Bitwise-or for union of bounded sets 01:16:21 : Step back and recap 01:26:15 : Tradeoff between number of hash bins and sparsity 01:29:12 : Conclusion Further reading: Po-Shen Loh. ”Flipping the Perspective in Contact Tracing” https://arxiv.org/abs/2010.03806