Dr. Stuart Bale spoke to MSRI’s Math Lovers Forum (mathlovers.msri.org) in May 2019. In this video recording, Dr. Bale explains some of what we’ve learned about the sun’s structure and gives an overview of NASA’s ongoing Parker Solar Probe mission, including some exciting new results.
Stuart Bale is a University of California, Berkeley professor of physics, former director of the campus’s Space Sciences Laboratory (SSL) and one of four principal investigators for the instruments aboard the Parker Solar Probe. In addition, his SSL research group participated in NASA’s STEREO mission studying the generation and evolution of Coronal Mass Ejection (CME) phenomena. Bale’s main research is focused on developing experiments to understand the role of plasma dynamics and magnetic fields in the large-scale evolution of astrophysical systems.
Markov chain Monte Carlo, or MCMC, is a powerful family of search algorithms that has applications all over science and engineering. I’ll make the case that it gives us the material for a major breakthrough in the study of redistricting: how do you decide when a map has been gerrymandered?
Moon Duchin is an Associate Professor of mathematics at Tufts University and serves as director of Tufts’ interdisciplinary Science, Technology, and Society program. Her mathematical research is in geometric group theory, low-dimensional topology, and dynamics. She is also one of the leaders of the Metric Geometry and Gerrymandering Group, a Tisch College-supported project that focuses mathematical attention on issues of electoral redistricting.
Duchin’s research looks at the metric geometry of groups and surfaces, often by zooming out to the large scale picture. Lately she has focused on geometric counting problems, in the vein of the classic Gauss circle problem, which asks how many integer points in the plane are contained in a disk of radius r. Her graduate training was in low-dimensional topology and ergodic theory, focusing on an area called Teichmüller theory, where the object of interest is a parameter space for geometric structures on surfaces.
Duchin has also worked and lectured on issues in the history, philosophy, and cultural studies of math and science, such as the role of intuition and the nature and impact of ideas about genius. She is involved in a range of educational projects in mathematics: she is a veteran visitor at the Canada/USA Mathcamp for talented high school students; has worked with middle school teachers in Chicago Public Schools, developed inquiry-based coursework for future elementary school teachers at the University of Michigan, and briefly partnered with the Poincaré Institute for Mathematics Education at Tufts.
Dr. Alessandro Chiesa will discuss the bitcoin privacy problem and how to fix it. He will introduce the main algorithmic ideas behind Bitcoin, the first decentralized crypto-currency to gain significant public trust and adoption.
Dr. Chiesa will further explain one of Bitcoin’s main limitations: its lack of privacy due to the fact that every payment is broadcast in plaintext. And he will conclude his discussion by explaining how to solve this problem with a beautiful cryptographic tool, zero knowledge proofs. This solution was recently deployed in the wild, as part of the cryptocurrency Zcash. Continue reading “Alessandro Chiesa: University of California, Berkeley”→
The gambler’s fallacy is the erroneous belief that if (for example) a coin comes up heads often, then in the next toss it is more likely to be tails. In Dr. Soundararajan’s recent work with Robert Lemke Oliver, they found that funnily enough, the primes exhibit a kind of gambler’s fallacy: for example, consecutive primes do not like to have the same last digit. Dr. Soundararajan will show some of the data on this, and explain what their research leads them to believe is happening. Continue reading “Kannan Soundararajan, Stanford University”→
Linear algebra is the foundation of scientific computing and its numerous applications. Yet, the world is nonlinear. In this lecture we argue that it pays off to work with models that are described by nonlinear polynomials, while still taking advantage of the power of numerical linear algebra. We offer a glimpse of applied algebraic geometry, by discussing current trends in tensor decomposition, polynomial optimization, and algebraic statistics. Continue reading “Bernd Sturmfels: University of California, Berkeley”→
Dr. Umesh Vazirani spoke to the Forum about the tremendous recent progress in the physical realization of devices based on the principles of quantum mechanics which also throw up a fundamental challenge: how to test quantum devices, which are by nature imperfect and susceptible to uncontrollable faults. Continue reading “Umesh Vazirani, University of California, Berkeley”→
Ramanujan’s work has had a truly transformative effect on modern mathematics, and indeed continues to do so as we understand further lines from his letters and notebooks. Dr. Bhargava presented some of the accessible gems of Ramanujan, and described some of the ways in which they have fundamentally changed modern mathematics (and indeed influenced our own work). Continue reading “Manjul Bhargava, Princeton University”→
Euler discovered how to assign a finite value to certain divergent sums, such as 1 + 2 + 4 + 8 + … that he determined should equal -1. How does one make sense of this?!? The 19th century mathematicians discovered a systematic approach to such madness. Contemporary number theorists have yet another approach, using an exotic number system that is not taught in schools. Dr. Conrad spoke to the Forum on how to calculate in this exotic world, and use it to understand a remarkable concrete fact about ordinary numbers. Continue reading “Brian Conrad, Stanford University”→