Bruce Kleiner, a principal investigator in the Simons Collaboration on Algorithms and Geometry, was also a 2014 Simons Fellow in Mathematics. He received a B.A and Ph.D. in mathematics from the University of California, Berkeley, and is currently a professor of mathematics at the Courant Institute of Mathematical Sciences at New York University.
“The things I’m working on now have roots in my own mathematical past and in mathematical history, but there are two or three main strands in my work,” says Kleiner. One of those “strands” involves the Ricci flow, a process in differential geometry that was famously used by Grigori Perelman to prove the Poincaré conjecture in dimension three. Kleiner received the National Academy of Sciences Award in 2013 for his work with John Lott, which provided a detailed account of Perelman’s solution to the conjecture.
Kleiner also conducts research in the field of metric geometry. There, his work is partly motivated by problems in computer science, which is “… one of the reasons I’m a part of the Simons Collaboration on Algorithms and Geometry,” says Kleiner, “and [that research] also has connections with symmetry and many other areas in mathematics.”
“I think of myself as a geometer, meaning the way I think about things is visual in nature. This kind of thinking is applicable to many different situations, including ones which don’t seem to have anything to do with geometry at all,” Kleiner says. For example, work on algorithms may be enhanced by this kind of dual analysis: an algorithm might look like a task to a computer, but one can view it differently, geometrically, considering it as something that is visual and that takes ideas from geometry, analysis of which might yield discoveries not evident before.
“The existence of [the Algorithms and Geometry] collaboration has been important to my work already… and will continue to be,” says Kleiner.