Cattani, Kaplan collaborated with Abel Prize-winning mathematician

During the course of his notable career, professor Pierre Deligne of the Institute for Advanced Study in Princeton, this year’s winner of the Abel Prize in Mathematics, collaborated with two members of the Department of Mathematics and Statistics: professors emeriti Eduardo Cattani and Aroldo Kaplan.

 

Deligne is being recognized “for seminal contributions to algebraic geometry and for their transformative impact on number theory, representation theory, and related fields.”

 

The Abel Prize was instituted in 2002 by the Norwegian Academy of Science and Arts as an international prize for outstanding scientific work in the field of mathematics. The prize is meant to recognize contributions of extraordinary depth and influence on the mathematical sciences. It carries a cash award of $1 million and is widely considered as the mathematical equivalent of the Nobel Prize.

 

The citation recognizing Deligne’s work highlights several of his scientific accomplishments including his joint work Cattani and Kaplan. In 1995, the three mathematicians published a paper titled “On the locus of Hodge classes.” In this paper they showed the algebraicity of a certain set which is, a priori, only analytically defined. This result constitutes strong evidence for the validity of the Hodge Conjecture, one of the central problems in algebraic geometry and one of the six remaining Millennium Problems proposed by the Clay Mathematics Institute at the start of this century.

 

Cattani said he was delighted, though not surprised, that Deligne had received the Abel Prize. “Deligne has been the leading figure in algebraic geometry for the past 40 years,” he said. “He picked up where Grothendieck left off and has carried the field to great heights. Kaplan and I felt that it was a great privilege to have been able to interact with him and to have been among the many recipients of his enormous mathematical generosity.”

 

Kaplan spoke in similar terms from Argentina, where he now resides, emphasizing “the combination of depth and simplicity that characterized Deligne’s ideas and his unpretentious demeanor.”