One UCSB professor was awarded a $50,000 grant for his contributions to algebraic geometry last week after he was recognized as an Alfred P. Sloan Foundation Research Fellow.
Assistant mathematics professor Paolo Cascini was one of 17 researchers from a University of California to receive the award. Along with the honor of being named a fellow, Cascini will receive a two-year, $50,000 grant to further his research. He said that much of his research concerns the Minimal Model Program.
“I have been working with my collaborators on the Minimal Model Program,” Cascini said. “The study of algebraic geometry involves algebraic varieties and algebraic manifolds, which are shapes with some kind of problem. The Minimal Model Program classifies these varieties.”
Cascini also said he believes the MMP is only 40 percent complete thus far. In his research statement, Cascini stated that the MMP is an important project, because it will allow future researchers to more easily identify items associated with the studied equations.
“In mathematics – as in many other sciences – it has always been very important to classify objects in a given context, because it makes them easier to study,” Cascini said. “Our [MMP] results are probably the best achievement in this direction.”
In his research thesis, Cascini stated that despite the ample amount of research conducted in this field, very little is known about “the classification of four-fold and higher dimensional varieties.” Four-fold refers to the number of dimensions in a geometric object, just as a line has one dimension and a surface and a plane has two dimensions. Advancements in MMP and related conjectures have the potential for advancing other theories and fields, such as the String Theory, which hypothesizes that elementary particles may look more like tiny vibrating objects. Previous theories viewed elementary particles as small points.
The Alfred P. Sloan Foundation is a philanthropic organization in New York established by former General Motors Chief Executive Officer Alfred P. Sloan, Jr. in 1934. This year, the foundation awarded almost $6 million to 118 scientist and researches in over 60 universities throughout the United States and Canada to study mathematics, economics, biology, chemistry and physics.