Featured Research

from universities, journals, and other organizations

Matroid theory: Mathematician solves 40-year-old problem

Date:
August 28, 2013
Source:
University of Waterloo
Summary:
A team of mathematicians has solved a problem first posed more than 40 years ago that has confounded modern mathematicians, until now.

A team of mathematicians has solved a problem first posed more than 40 years ago that has confounded modern mathematicians, until now.

Professor Jim Geelen of the University of Waterloo and his colleagues, Professor Bert Gerards of Centrum Wiskunde & Informatica and the University of Maastricht in the Netherlands, and Professor Geoff Whittle of Victoria University of Wellington in New Zealand have proved the famous Rota's Conjecture.

The three men worked for almost 15 years to solve this problem posed by the famous mathematician and philosopher Gian-Carlo Rota in 1970. Earlier this year, in Waterloo, the trio completed the final step in their epic project.

Rota's Conjecture relates to a specialized area of mathematics known as matroid theory, a modern form of geometry, which was pioneered by the mathematician Bill Tutte.

The theory investigates the embedding of abstract geometric structures, or matroids, into concrete geometric frameworks - namely, projective geometries over a given finite field. The conjecture is that, for each finite field, there is a finite set of obstructions preventing such a realization. The conjecture was posed by Rota at the International Congress of Mathematics in 1970, serendipitously, one week before Geelen was born.

"For me the most rewarding part of the research project has been the collaboration with Bert and Geoff. We work together about three times a year typically for periods of three weeks either here in Waterloo or in New Zealand or the Netherlands," said Professor Geelen. "Those visits are intense; we sit in a room together, all day every day, in front of a whiteboard. The discussion can be very lively at times, while at other times, when we are stuck, we might sit there for two hours without saying a word; each just thinking about ways to overcome the particular obstacle."

In 1999, Geelen, Gerards and Whittle joined forces to work on Rota's Conjecture as well as generalizing the famous Graph Minor Theory developed by Robertson and Seymour to matroids.

Last year they completed their Matroid Minor Theory which gives deep insights into the structure of matroids. The proof of Rota's Conjecture relies on the full power of that theory and, in addition, required groundbreaking new results on matroid connectivity.

According to the trio, the real hard work only just began when early this year they started writing up the results of their work. The Graph Minors Theory itself filled more than 600 journal pages and the Matroid Minors Theory is set to be at least as long. The team expects that it will take them at least three years to complete the writing.

Jim Geelen is a Professor in the Department of Combinatorics and Optimization at the University of Waterloo and holds a Canada Research Chair.  


Story Source:

The above story is based on materials provided by University of Waterloo. Note: Materials may be edited for content and length.


Cite This Page:

University of Waterloo. "Matroid theory: Mathematician solves 40-year-old problem." ScienceDaily. ScienceDaily, 28 August 2013. <www.sciencedaily.com/releases/2013/08/130828092304.htm>.
University of Waterloo. (2013, August 28). Matroid theory: Mathematician solves 40-year-old problem. ScienceDaily. Retrieved September 30, 2014 from www.sciencedaily.com/releases/2013/08/130828092304.htm
University of Waterloo. "Matroid theory: Mathematician solves 40-year-old problem." ScienceDaily. www.sciencedaily.com/releases/2013/08/130828092304.htm (accessed September 30, 2014).

Share This



More Computers & Math News

Tuesday, September 30, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Apple Releases 'Shellshock' Fix Despite Few Affected Users

Apple Releases 'Shellshock' Fix Despite Few Affected Users

Newsy (Sep. 29, 2014) — Apple released a security fix for the "Shellshock" vulnerability Monday, though it says only "advanced UNIX users" of OS X need it. Video provided by Newsy
Powered by NewsLook.com
Do Video Games Trump Brain Training For Cognitive Boosts?

Do Video Games Trump Brain Training For Cognitive Boosts?

Newsy (Sep. 29, 2014) — More and more studies are showing positive benefits to playing video games, but the jury is still out on brain training programs. Video provided by Newsy
Powered by NewsLook.com
New Facebook Ad Platform Goes Where You Go On The Web

New Facebook Ad Platform Goes Where You Go On The Web

Newsy (Sep. 29, 2014) — Called Atlas, the platform allows advertisers to place ads based on Facebook info on sites outside of Facebook. Video provided by Newsy
Powered by NewsLook.com
Google Tightens Requirements For Android Manufacturers

Google Tightens Requirements For Android Manufacturers

Newsy (Sep. 27, 2014) — Phonemakers who want to use Google’s software in their devices will have to stick to more stringent requirements. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:

Strange & Offbeat Stories

 

Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins