University of Calgary

World renowned mathematicians to visit Banff, study ‘Whitney problems’

UToday HomeApril 11, 2013

By Devon Lavigne

Banff International Research StationThe Banff International Research Station is located on the campus of The Banff Centre. BIRS occupies Corbett Hall and the TransCanada Pipelines Pavilion. Photo courtesy Banff International Research StationNot everyone comes to the Canadian Rockies to snowboard. Some visitors, mathematicians from around the world, will spend a week hunkered down working on “Whitney problems.”

Nestled in picturesque Banff is the Banff International Research Station for Mathematical Innovation and Discovery (BIRS).

Inspired by other international mathematical institutes, such as the Mathematisches Forschungsinstitut Oberwolfach in Germany’s Black Forest, and the Centre International de Rencontres Mathematiques in Luminy, France, BIRS is the culmination of the efforts of Canadian and American scholars to create a North American institute as renowned as those in Germany and France.

From April 21 to 26, international experts will descend on Banff to take part in the Focus on Whitney Problems week at the institute.

Hassler Whitney’s 1934 research into function theory posed what is now called Whitney’s Problem: Can we determine whether a function on an arbitrary subset of Euclidean space is extendible to a function of a prescribed smoothness on the whole space?

University of Calgary’s head of Mathematics and Statistics, professor Michael Lamoureux, puts it in layman’s terms: “Imagine taking a picture of a mountain range (e.g. like in Banff), but where lots of the mountain is obscured by clouds. In the picture, there are only portions of the mountain visible,” he explains.

“The question is how can we ‘fill in’ the picture to complete the mountain range, where the new part of the mountains you fill in looks as smooth (or as rough) as the original part of the mountain,” he adds. “And what if the clouds reveal only a tiny or jagged part of the mountain? Can you still do it? Dress it up with a lot of technical conditions? This is the Whitney problem,” concludes Lamoureux.

The Whitney Problem week is organized by professors Alex Brudnyi (University of Calgary), Charles Fefferman (Princeton), Pierre Milman (University of Toronto) and Nahum Zobin (College of William and Mary), and will see many highly regarded mathematicians — including Fields medalists, mathematics’ version of the Nobel Prize — among the participants. They will be invited to pose problems and questions beforehand on the program’s website.

The week will finish with a colloquium at the University of Calgary April 26, given by Nahum Zobin, on the topic of Whitney problems and their quantization.

 

Follow UToday on Twitter.
Check the UToday website for news about events, people and trends at University of Calgary.
Follow what’s happening on campus using our interactive calendar.