Research Highlights

SAMSI Kicks Off 2017-2018 Programs on Environment and High-Dimensional Data Sampling

SAMSI - October 2017

Richard Smith, Director of SAMSI, opens the CLIM Opening Workshop at the N.C. Biotechnology Center on Aug. 21, 2017. The workshop marks the beginning of the CLIM Program, focused on using data and climate models to analyze environmental changes on our Earth. Much like universities around the country beginning their fall semesters, SAMSI also kicked off their 2017-2018 year-long programs’...

Graduate Students get Practical Experience in Math and Statistics Research at 2017 IMSM

SAMSI - October 2017

A graduate student and her group present findings on a problem posed by one of the many program partners at the 2017 IMSM Workshop on the campus of North Carolina State University from July 17-26. The workshop exposes graduate students to methods used by industry and national labs to solve real world problems. SAMSI completed the 2017 Industrial Math/Stat Modeling Workshop for Graduate Students...

Trisections

AIM - October 2017

Understanding four dimensional structures or manifolds is both a mysterious and complex task. The goal of the AIM workshop ‘Trisections and low-dimensional topology’ held in March of 2017 was to study these four dimensional objects with a new perspective introduced by David Gay and Robion Kirby in 2012. In three dimensions it has been known for a fairly long time that closed manifolds can be...

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Waves, Kakeya sets, and Diophantine equations

MSRI - June 2017

Ciprian Demeter A central problem in Physics is to understand the complicated ways in which waves can interact with one another. The field of Harmonic Analysis grew out of the observation that any natural signal that is periodic in time can be built by superimposing simple waves with whole number frequencies. In geometric optics, quantum mechanics, and the study of water waves, we must...

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SAMSI Brings Astronomers and Statisticians Together to Study Universe

SAMSI - June 2017

Contributed by: Jim Barrett, Ph.D. student, School of Physics & Astronomy, University of Birmingham, UK Maya Fishbach, Ph.D. student, Department of Astronomy and Astrophysics, University of Chicago, USA Bo Ning, Ph.D. candidate, Department of Statistics, North Carolina State University, USA Daniel Wysocki, Ph.D. student, School of Physics & Astronomy’s Astrophysical Sciences & Technology...

Visualizing PML

ICERM - September 2016

Visualizing PML David Dumas and François Guéritaud On the surface of a sphere, every simple closed curve (that is, a curve that starts and ends at the same point and which does not cross itself) forms the boundary of a disk, i.e. a contiguous region without holes. In this sense, the sphere has only one “type” of simple closed curve. In contrast, on a surface with a more complicated...

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Special Year on Geometric Structures on 3-Manifolds

IAS - September 2016

During the 2015-16 academic year, the School of Mathematics conducted a special program on Geometric Structures on 3-Manifolds. The program was led by Distinguished Visiting Professor Ian Agol of the University of California at Berkeley. The theme of the program was classication of geometric structures on 3-manifolds. Twenty members took part in the program. Senior members included David Gabai,...

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NET Maps

AIM - July 2016

It is human nature to try to classify things—that is, to sort them into organized types. Many of the central problems in mathematics are problems of classification of various types of related mathematical objects. The classification of finite groups, for example, was a landmark accomplishment of the last century, and the classification of manifolds continues to challenge topologists. The AIM...

Big Data meets Number Theory

ICERM - May 2016

Researchers from ICERM’s special semester “Computational Aspects of the Langlands Program” are creating new data-driven models for collaborative research in number theory, culminating in the May 10, 2016 official release of the L-functions and Modular Forms Database (LMFDB) at www.lmfdb.org. Computation is not new to number theory – in Babylon huge tablets of sines and cosines were created and...

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Identifying Links Between the S&P500 and VIX Derivatives

IPAM - April 2016

By Andrew Papanicolaou The technique of volatility trading has been common practice since the 1970’s. Typically, a long (short) position in volatility included a long (short) position in options. In 2003 there came a more standardized way of trading volatility, as the VIX formula became the universally-accepted predictor of volatility. The VIX is a 30-day predictor of volatility given by a...