. 24/7 Space News .
TECH SPACE
Exploring the mathematical universe
by Staff Writers
San Jose CA (SPX) May 12, 2016


A nonholomorphic modular form is one of the many types of objects in the LMFDB. Image courtesy Fredrik Stroemberg. For a larger version of this image please go here.

team of more than 80 mathematicians from 12 countries has begun charting the terrain of rich, new mathematical worlds, and sharing their discoveries on the Web. The mathematical universe is filled with both familiar and exotic items, many of which are being made available for the first time. The "L-functions and Modular Forms Database," abbreviated LMFDB, is an intricate catalog of mathematical objects and the connections between them.

Making those relationships visible has been made possible largely by the coordinated efforts of a group of researchers developing new algorithms and performing calculations on an extensive network of computers. The project provides a new tool for several branches of mathematics, physics, and computer science.

A "periodic table" of mathematical objects
Project member John Voight, from Dartmouth College, observed that "our project is akin to the first periodic table of the elements. We have found enough of the building blocks that we can see the overall structure and begin to glimpse the underlying relationships." Similar to the elements in the periodic table, the fundamental objects in mathematics fall into categories.

Those categories have names like L-function, elliptic curve, and modular form. The L-functions play a special role, acting like 'DNA' which characterizes the other objects. More than 20 million objects have been catalogued, each with its L-function that serves as a link between related items. Just as the value of genome sequencing is greatly increased when many members of a population have been sequenced, the comprehensive material in the LMFDB will be an indispensible tool for new discoveries.

The LMFDB provides a sophisticated web interface that allows both experts and amateurs to easily navigate its contents. Each object has a "home page" and links to related objects, or "friends." Holly Swisher, a project member from Oregon State University, commented that the friends links are one of the most valuable aspects of the project: "The LMFDB is really the only place where these interconnections are given in such clear, explicit, and navigable terms. Before our project it was difficult to find more than a handful of examples, and now we have millions."

Experimental mathematics for the 21st century
Mathematics has always been an experimental science: conjectures are formulated and tested based on evidence of all kinds. As we enter a new century of research, large-scale computer experiments now take the place of hand calculations, with the effect of accelerating the process of testing and discovery.

John Jones, from Arizona State University, described this motivation for the project: "Many of us have made extensive computations, and we wanted to make this data available to other researchers and to link these projects together to aid mathematical progress. By joining forces, we now have a site for one-stop shopping of big data."

Many of these calculations are so intricate that only a handful of experts can do them, and some computations are so big and take so long that it makes sense to only do them once. The LMFDB also includes an integrated knowledge database that explains its contents and the mathematics behind it. Project member Brian Conrey, Director of the American Institute of Mathematics, thinks that the LMFDB approach is the wave of the future: "We are mapping the mathematics of the 21st century. The LMFDB is both an educational resource and a research tool which will become indispensable for future exploration."

According to Benedict Gross, an emeritus professor of mathematics at Harvard University, "Number theory is a subject that is as old as written history itself. Throughout its development, numerical computations have proved critical to discoveries, including the prime number theorem, and more recently, the conjecture of Birch and Swinnerton-Dyer on elliptic curves.

"During the past fifty years, modular forms and their L-functions have taken center stage at the forefront of number theory. The LMFDB pulls together all of the amazing computations that have been done with these objects. Having this material accessible in a single place will provide an invaluable resource for all of us working in the field."

Prime numbers have fascinated mathematicians throughout the ages. The distribution of primes is believed to be random, but proving this remains beyond the grasp of mathematicians to date. Under the Riemann hypothesis, the distribution of primes is intimately related to the Riemann zeta function, which is the simplest example of an L-function.

The LMFDB contains more than twenty million L-functions, each of which has an analogous Riemann hypothesis that is believed to govern the distribution of wide range of more exotic mathematical objects. Patterns found in the study of these L-functions also arise in complex quantum systems, and there is a conjectured to be direct connection to quantum physics.

Massive computations in the cloud
The scale of the computational effort involved in the LMFDB is staggering: a total of nearly a thousand years of computer time spent on calculations by multiple teams of researchers. A recent contribution by Andrew Sutherland at MIT used 72,000 cores of Google's Compute Engine to complete in one weekend a tabulation that would have taken more than a century on a single computer. As noted by Sutherland, "computations in number theory are often amenable to parallelization, and this makes it easy to scale them to the cloud." The application of large-scale cloud computing to research in pure mathematics is just one of the ways in which the project is pushing forward the frontier of mathematics.

History of the LMFDB
The idea of pooling the computational results of researchers in several areas of mathematics was started at a workshop at the American Institute of Mathematics in 2007. Work on the LMFDB began at a workshop supported by the National Science Foundation (NSF) in 2010.

The majority of the work on the LMFDB was done at subsequent workshops supported by the NSF and by the Engineering and Physical Sciences Research Council (EPSRC) in the UK through a Programme Grant awarded jointly to Warwick and Bristol Universities, as well as at long-term programs at the Mathematical Sciences Research Institute (MSRI) in Berkeley, CA, and the Institute for Computational and Experimental Research in Mathematics (ICERM) in Providence, RI. More than 100 research papers reference the data in the LMFDB.


Thanks for being here;
We need your help. The SpaceDaily news network continues to grow but revenues have never been harder to maintain.

With the rise of Ad Blockers, and Facebook - our traditional revenue sources via quality network advertising continues to decline. And unlike so many other news sites, we don't have a paywall - with those annoying usernames and passwords.

Our news coverage takes time and effort to publish 365 days a year.

If you find our news sites informative and useful then please consider becoming a regular supporter or for now make a one off contribution.
SpaceDaily Contributor
$5 Billed Once


credit card or paypal
SpaceDaily Monthly Supporter
$5 Billed Monthly


paypal only


.


Related Links
American Institute of Mathematics
Space Technology News - Applications and Research






Comment on this article via your Facebook, Yahoo, AOL, Hotmail login.

Share this article via these popular social media networks
del.icio.usdel.icio.us DiggDigg RedditReddit GoogleGoogle

Previous Report
TECH SPACE
Accelerating complex computer simulations: thinking beyond ones and zeros
Washington DC (SPX) May 10, 2016
Whether designed to predict the spread of an epidemic, understand the potential impacts of climate change, or model the acoustical signature of a newly designed ship hull, computer simulations are an essential tool of scientific discovery. By using mathematical models that capture the complex physical phenomena of the real world, scientists and engineers can validate theories and explore s ... read more


TECH SPACE
NASA research gives new insights into how the Moon got inked

First rocket made ready for launch at Vostochny spaceport

Supernova iron found on the moon

Russia to shift all Lunar launches to Vostochny Cosmodrome

TECH SPACE
Flying observatory detects atomic oxygen in Martian atmosphere

Beyond Ikea: Swedish Gadget to Harvest Water on Martian Surface

Clues about Volcanoes Under Ice on Ancient Mars

Second ExoMars mission moves to next launch opportunity in 2020

TECH SPACE
NASA makes dozens of patents available in public domain

Thornton leads upgrade of ground special power for Orion

How will people interact with technology in the future

Pentagon's research agency showcases future tech

TECH SPACE
Long March-7 rocket delivered to launch site

China's space technology extraordinary, impressive says Euro Space Center director

China can meet Chile's satellite needs: ambassador

China launches Kunpeng-1B sounding rocket

TECH SPACE
NASA, Space Station partners announce future mission crew members

New landing date for ESA astronaut Tim Peake

Tim Peake goes roving

Russia delays space crew's return to Earth

TECH SPACE
SpaceX's Dragon cargo ship splashes down in Pacific

Date set for second SLS booster test

First work platforms powered tested in VAB for Space Launch System

SpaceX successfully lands rockets first stage after space launch

TECH SPACE
Synchronized planets reveal clues to planet formation

NASA says 1,284 new planets found by Kepler telescope

Kepler space telescope finds another 1284 exo planets

Scientists discover potentially habitable planets

TECH SPACE
Design tool enables novices to create bendable input devices for computers

Molybdenum disulfide holds promise for light absorption

Accelerating complex computer simulations: thinking beyond ones and zeros

Machine learning accelerates the discovery of new materials









The content herein, unless otherwise known to be public domain, are Copyright 1995-2024 - Space Media Network. All websites are published in Australia and are solely subject to Australian law and governed by Fair Use principals for news reporting and research purposes. AFP, UPI and IANS news wire stories are copyright Agence France-Presse, United Press International and Indo-Asia News Service. ESA news reports are copyright European Space Agency. All NASA sourced material is public domain. Additional copyrights may apply in whole or part to other bona fide parties. All articles labeled "by Staff Writers" include reports supplied to Space Media Network by industry news wires, PR agencies, corporate press officers and the like. Such articles are individually curated and edited by Space Media Network staff on the basis of the report's information value to our industry and professional readership. Advertising does not imply endorsement, agreement or approval of any opinions, statements or information provided by Space Media Network on any Web page published or hosted by Space Media Network. General Data Protection Regulation (GDPR) Statement Our advertisers use various cookies and the like to deliver the best ad banner available at one time. All network advertising suppliers have GDPR policies (Legitimate Interest) that conform with EU regulations for data collection. By using our websites you consent to cookie based advertising. If you do not agree with this then you must stop using the websites from May 25, 2018. Privacy Statement. Additional information can be found here at About Us.