Gravitational Waves

A simulation of the merger of two black holes and the resulting emission of gravitational radiation.

Credit: NASA/C. Henze

The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry C. Barish, and Kip S. Thorne for their work on the detection of gravitational waves. (See Note 1.)  The physics and engineering that go into this accomplishment are truly impressive.  However, before anyone could imagine setting up the experiment, some mathematical questions needed to be answered.  There are two articles in the August 2017 issue of the AMS Notices that give an overview the mathematics of gravitational waves.  In this post, I crib from those two articles and provide a literature tour of some of the significant papers by relying on MathSciNet. A longer article by Bieri just published in the AMS Bulletin goes into more detail on a selection of the topics.   Continue reading

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Emmanuel Candès – MacArthur Fellow

Photo of Emmanuel Candès

Emmanuel Candès (Source Wikimedia)

Emmanuel Candès has won a prestigious MacArthur Fellowship.  The official announcement is here.  The LA Times has a nice write-up.   Both the Los Angeles Times and the MacArthur announcement highlight Candès’s work on compressed sensing.  Terry Tao has a spot-on reaction to this work, quoted in the LA Times, typical of most mathematicians when you first hear about the method:  you can’t be getting be getting something for nothing.  This can’t work.  But it does!  Tao finally came around to believe it, as has the rest of the world.   Continue reading

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Job Posting – Associate Editor at Mathematical Reviews

Work at Math ReviewsMathematical Reviews is hiring!  We are looking for a new Associate Editor to start in late spring or summer 2018.  The new editor should have expertise in algebra and an interest in a range of algebraic topics, such as representation theory, nonassociative algebras, and group theory.  The job announcement is on the AMS website:  http://www.ams.org/about-us/AssociateEditor.pdf.  The position is posted on mathjobs.org: https://www.mathjobs.org/jobs/jobs/10667, which is also where you can submit an application.

Mathematical Reviews is a great place to work.  You get to do something important and useful.  You would also be working with great people.  A list of the current editors is here.  And here is a picture of some of us observing the eclipse in August 2017. Math Reviews watching the Eclipse of 2017

If you have any questions, drop me a line.

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MathSciNet at the MCA in Montreal

MCA 2017 banner

I just came back from the Mathematical Congress of the Americas in Montreal.   It was an intense week of mathematics.  Besides having excellent invited and plenary lectures, there were 70 special sessions!  There were five plenary lectures:  Manuel del Pino (Universidad de Chile); Shafrira Goldwasser (MIT); Peter Ozsvath (Princeton University); Yuval Peres (Microsoft Research); and Kannan Soundararajan (Stanford University).  Erik Demaine (Massachusetts Institute of Technology) and Étienne Ghys (École Normale Supérieure de Lyon) gave well-received public lectures.  The list of invited speakers is here.   Continue reading

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Maryam Mirzakhani

 

Maryam MirzMaryam Mirzakhani at ICM 2014akhani is known for her work on moduli spaces of Riemann surfaces.  Some of her most cited work looks at the moduli space of a genus $g$ Riemann surface with $n$ geodesic boundary components.  In two of her papers, she computes the volume of these moduli spaces, with respect to the Weil-Petersson metric (see below).  In another, she provides a means for counting the number of simple closed geodesics of length at most $L$. Mirzakhani is also known for her work on billiards (see the review of her paper with Eskin and Mohammadi below), a subject closely related to moduli space questions.  Teichmüller theory and the geometry of moduli spaces are famously deep subjects.  Making progress requires mastering large areas of analysis, dynamical systems, differential geometry, algebraic geometry, and topology.  I can only appreciate Mirzakhani’s work superficially, as I have not mastered those subjects.   Instead, some reviews of her work are reproduced below.   Continue reading

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Laure Saint-Raymond

Laure Saint-RaymondLaure Saint-Raymond is a mathematician working in partial differential equations, fluid mechanics, and statistical mechanics.  She is a professor at l’École Normale Supérieure de Paris and the Université Pierre et Marie Curie (also known as Paris VI).  In 2013, she became the youngest member ever elected to the French Academy of Sciences, in the Mechanics and Computer Science section, where several other top-notch mathematicians are members.   Continue reading

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Yves Meyer wins the Abel Prize

Yves Meyer has been selected to win the 2017 Abel Prize.  The citation is “for his pivotal role in the development of the mathematical theory of wavelets”.  His work is certainly well known within mathematics, especially within harmonic analysis and in its important applications in image processing, data compression, signal analysis, and many other modern settings.    Continue reading

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Karen Smith

Karen Smith, Albuquerque AMS Sectional, April 2014Karen Smith is a mathematician at the University of Michigan, which is where she also did her Ph.D.  Her thesis was on tight closure, an important topic in commutative algebra.  There is, of course,  a lot of overlap between commutative algebra and algebraic geometry, and Smith’s publications demonstrate this mix with about three quarters of them being in commutative algebra and a quarter in algebraic geometry.  Her publications are also a good demonstration of the collaborative nature of mathematics.  Continue reading

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Quanta Magazine

Quanta Magazine, from the Simons Foundation, has been publishing some excellent articles about mathematics.  It is not a research journal, so Mathematical Reviews doesn’t cover it.  Nevertheless, if you want to dig deeper into some of the mathematical issues discussed in their articles, MathSciNet is a great tool for doing so.

Continue reading

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#Citations

Picture of a Chevrolet CitationMathematicians are good at counting.  We can count the number of ways to roll  a 7 with two dice.  (Answer = 6.) We can count the number of ways to shuffle a deck of cards so that every card is not in its original position.  (Answer = $!52$ = 29672484407795138298279444403649511427278111361911893663894333196201.)  We can count the number of lines on a cubic surface in $\mathbf{CP}^3$. (Answer = 27.)   Sometimes we can count, but we don’t really know what the actual number is, such as when we count the minimum number of guests that must be invited so that at least $m$ will know each other or at least $n$ will not know each other.  (Answer = the Ramsey number $R(m, n)$.)  Many times, it is better to use an asymptotic estimate, such as Stirling’s formula.  When we can’t estimate, we can bound, such as Conrey’s result that more than two-fifths of the zeros of the Riemann zeta function are on the critical line.  Lately, we (along with our colleagues in other disciplines) have started counting citations.   Continue reading

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