D’port woos Field medalist to Tea

Two Davenport students proved Friday that a little e-mail can go a long way.

After electronically enlisting the help of Fields Medalist and Princeton professor Vladimir Voevodsky with a mathematical puzzle, Olga Lopusiewicz ’05 and Wei Deng ’05 decided to invite Voevodsky, or “Vlad” as the two girls have come to call him, to a Master’s Tea in Davenport College.

“We decided to e-mail a math genius and he actually e-mailed us back,” Deng said.

At the talk, Voevodsky spoke about how he initially was interested in physics and realized that mathematics would be necessary to better understand the subject. As his studies continued, Voevodsky said he became aware of gaps in mathematical theory.

“For a while I was reading more involved books in calculus and was getting extremely bored,” he said. “I started to realize that there is a very large gap between pure and applied mathematics and it is not filled with an intermediate stage.”

Voevodsky was awarded the Fields Medal in mathematics this past August in Beijing, China. He won the award for solving the Milnor conjecture, which was one of the major problems in algebraic geometry. The Fields Medal is the highest scientific award that can be given to mathematicians and has come to be known as “the Nobel Prize of mathematics.”

The medal, which recognizes existing mathematical work as well as the prospect of future achievement, has been awarded every four years since 1936 and is only awarded to mathematicians for research completed before the age of 40. This limit is set in part to give younger mathematicians the chance to be recognized for their work even if they do not have seniority in their fields.

Voevodsky said that the first place he had seen the definition of a category was in Yale mathematics professor Serge Lang’s textbook. Categories are a way to describe seemingly unrelated collections of objects in order to give them a common mathematical treatment.

“Category theory is the main bridge to connect the two types of mathematics,” Voevodsky said. “Instead of considering mathematical structures by what they consist of, you consider them by how they interact with the objects of the same sort in a group.”

This assertion is the basis for Voevodsky’s work and his development of a new cohomology theory for algebraic theories. Cohomologies are chains of groups or rings — mathematical objects describing symmetry — that group together specific algebraic objects, allowing one to characterize them, know them better and help differentiate them from other structures.

“The idea was to develop cohomology of these systems of algebraic equations,” Voevodsky said.

Voevodsky later went on to use this basis to help him prove the Milnor conjecture, which established the connection between the innate properties of numbers and the study of higher-dimensional curved surfaces.

“What really catches the eye are results,” Voevodsky said. “Results in mathematics are to prove what no one else has been able to prove. The Milnor conjecture took a couple of years. Then it was solved. Then it made a splash.”

Voevodsky said he credits one of his predecessors, Alexandre Grothendieck, a 1966 Fields Medalist, for his revolutionary work in the field of algebraic geometry.

“[Grothendieck] is outstanding,” Voevodsky said. “He basically built a whole field from scratch.”

When asked if his life has changed much since receiving the Fields Medal, Voevodsky said his life has remained generally the same.

“It didn’t change much in my professional life,” Voevodsky said. “But as far as e-mails — just one.”