Invariants of Three-Manifolds

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This may come as a blow to Star Trek fans, but wormholes cannot be formed—at least according to new research done at the University of Calgary.

An international conference, Invariants of Three-Manifolds, will be held at Kananaskis this week to study research and find new methods for comprehending the mathematical nature of the universe.

According to U of C Physics professor and conference co-organizer Dr. David Hobill, invariants and manifolds are very complicated.

"There are different types of invariants," said Hobill. "One way of looking at it is to ask yourself what quantities will always remain the same regardless of what you do."

The abstract concept invariants can be expressed with very complicated algebraic equations. The term three manifolds simply means three dimensional space.

"We’re interested in three dimensional space because that’s the kind of space we live in," said Hobill.

The conference is being held near Calgary because the calculations needed to understand the relationship between invariants and physics are being done at the U of C by John Bryden, Peter Zvengrowski, Claude Hayat-Legrand and Heiner Zieschang.

"They realized their approach to solving problems in topology [the overall structure of objects] could be used to actually calculate these invariant quantities in field theories," said Hobill.

Hobill believes the aim of the conference is to strengthen and clarify the relationship between mathematics and physics. U of C Mathematics professor and conference co-organizer Dr. John Bryden agrees.

"The basic idea is to try and bring together people concerned with three manifolds, but having different areas of expertise," said Bryden. "We could pool all our knowledge and therefore try to help develop new ideas to deal with these manifolds."

Bryden hopes this conference will help scientists understand the nature of these invariants.

"You might find some objects that look very similar to each other, but how do you in fact prove mathematically that they are not the same?" he said.

Conference funding is provided by the Pacific Institute for Mathematical Science, the University Research Grants Committee, and Dean of the Faculty of Science, Mike Boorman.

"[Boorman] sees this as a way of helping the research that goes on within this university to get a larger international stature," said Hobill. "We’ve brought in a large number of well-known international physicists and mathematicians and by helping cover the cost of bringing people here, it helps the reputation of the U of C."

One of the speakers at the conference will be leading mathematician Vladimir Turaev, who believes the interest in the theory lies in how it unites very different areas of mathematics which were previously thought to be disjointed.

"Some of the theories are very recent; they are 15 years old or less," he said. "And some of them are relatively old. So the many different areas of mathematical and theoretical physics come together to give a solution to… a specific mathematical question."