Moon Duchin: Tufts University

Random Walks and Gerrymandering

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?

Math Lovers Forum at MSRI: Moon Duchin on “Random Walks and Gerrymandering” from MSRI on Vimeo.


DuchinMoon 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.

Krzysztof Burdzy: University of Washington, Seattle

The least interesting philosophical theory of probability ever (but at least it makes sense)

I will present a new way to look at the scientific laws of probability. I will argue that:
(i) The existing philosophy of probability is a complete intellectual failure.
(ii) The two most popular philosophical theories of probability formalize
only those beliefs that were never disputed.
(iii) The non-formalized parts of probability are swept under the rug of absurdities.
(iv) Even the justifications of the non-controversial beliefs are nonsensical.
You can watch the event video below.

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Alessandro Chiesa: University of California, Berkeley

Bitcoin, Its Privacy Problem and How to Fix It

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.
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Kannan Soundararajan, Stanford University

Primes Fall for the Gambler’s Fallacy

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.
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Bernd Sturmfels: University of California, Berkeley

 

Beyond Linear Algebra

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”

Manjul Bhargava, Princeton University

Ramanujan’s Gems

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”

Brian Conrad, Stanford University

P-adic Numbers

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.
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Cédric Villani, Institut Henri Poincaré

Of Planets, Stars and Eternity

After Newton’s great achievements, it seemed to scientists and philosophers of the Enlightenment that we should be able to predict everything about the future of the physical world from a knowledge of its present state. One of the areas where that should be  easiest is to predict the future of the solar system, and indeed our ability to predict the motions of the planets in the short term is extremely good. But what about the long term? Can we even say whether our planets will someday be thrown far from the sun by the cumulative forces of gravitational perturbations?

This problem has occupied mathematicians since the 19th century, and has led to great advances in our understanding of dynamical systems — but the original question remains open. Prof. Villani  spoke to the Forum about the study of the long time behavior of such systems from, from the Solar system itself to galaxies and related questions from fluid mechanics.
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