World leading mathematicians to solve mysteries at the interface of geometry and topology | Mathematics - Department of Mathematical Sciences

An array of fundamental and unanswered questions in mathematics lie at the intersection of geometry and topology by Department of Mathematical Sciences at University of Copenhagen.

Professor Nathalie Wahl
Photo: Jacob Helbig/University of Copenhagen

With a 60 million kroner grant from the Danish National Research Foundation to establish a new research center, University of Copenhagen mathematicians hope to solve a few of these decades-old problems.

For a bird, there is only one shortest route between Copenhagen and New York, while there are infinitely many shortest routes between the North and the South Pole. This is because the earth is round, not flat. But what happens if one instead can only travel by boat or road? Or, what if "shortest" is to be interpreted as "cheapest" or "least CO₂-emitting"? These are a few of the questions that a group of mathematicians from the University of Copenhagen in Denmark will strive to answer.

In abstract terms, it is about optimizing a geometric problem: "the shortest path". And the example of shortest paths from the North Pole to the South Pole shows that the answer is closely related to the basic "form" or topology of the object considered.

A team of world leading mathematicians from the University of Copenhagen’s Department of Mathematical Sciences, headed by Professor Nathalie Wahl, will, with a 60.2 million kroner grant from the Danish National Research Foundation, establish a new research center geared to address fundamental scientific problems such as these that lie at the interface of the fields of geometry and topology.

From forest fires to airbags Despite being fundamental mathematical research, there are plenty of potential applications. The 43-year-old Oxford-educated mathematician Nathalie Wahl explains:

"While these mathematical questions are abstract in essence, they are also applicable in practice in numerous contexts. For example, if you seek to calculate how a forest fire will spread, how an airbag inflates, or how space expands – each of these things can be considered as geometric objects that change shape over time. They are all controlled by the same types of equations."...

"The University of Copenhagen is already among the world’s best in the field of topology. This grant gives us the chance to attain a similar level in geometry. By bringing the disciplines nearer to one another, we expect to achieve significant progress in solving fundamental problems at the overlap of these two branches of mathematics," says Nathalie Wahl...

The Copenhagen Center for Geometry and Topology (GeoTop) will open in 2020. It will be located at the Department of Mathematical Sciences at the University of Copenhagen.
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Source: Department of Mathematical Sciences