The latest “addition” to the mathematical field of low-dimensional topology derives from the 5Cs. Joshua Greene HM ’02 won the American Mathematical Society’s (AMS) 2023 Levi L. Conant Prize with his article on Heegaard Floer homology, cited to become a “canonical reference for experts and non-experts alike.”
The Levi L. Conant Prize recognizes the “best expository paper published in either the Notices of the AMS or the Bulletin of the AMS in the preceding five years,” according to the AMS website.
“I am very proud to receive the recognition, although my work being singled out amongst so many wonderful articles makes me feel a bit sheepish, too,” Greene told TSL via email. “ … I knew that it would be a very time-consuming effort, but I saw it as a great honor and professional opportunity to do so, and so I seized it.”
After graduating from Harvey Mudd College with distinction and mathematics departmental honors, Greene served as a volunteer in Americorps with Habitat for Humanity. He then returned to academia, with a Masters in Science from the University of Chicago in 2004, a doctorate from Princeton University in 2009 and a post-doctorate at Columbia University.
Now, Greene is a faculty member at Boston College doing research in low-dimensional topology.
“I owe a lot to my formation and teachers at Harvey Mudd College for this award,” Greene said via email. “There is such a strong emphasis on quality of communication which comes through in the training and coursework at Mudd, and I have been very well set up in my career, thanks to it. Take advantage of it while you are there — it is a very special atmosphere!”
First interested in combinatorics and topology as a student at Harvey Mudd, Greene said he knew he would study either one in graduate school. During his time at Princeton, he attended a course about Heegaard Floer homology taught by his future adviser.
“The field appealed to me because it was a fresh area,” Greene said. “It felt like a place where I could combine my interests and make my own inroads, and I knew it would also challenge me to learn a lot of material well beyond my comfort zone.”
While topology is a relatively new field, it’s still about two centuries old.
“For me, the main problem was the abundance of excellent papers that had already been written on the subject!” Greene said. “It made it difficult for me to conceive of how to expose the area in a different or useful way.”
In the end, Greene focused on devising a piece that he would have liked to encounter as a newcomer to the study.
“That involved putting the subject into a wider context, describing the historical antecedents which led to its creation, emphasizing recurring themes and describing what were, to me, the most exciting aspects of the subject, without going deeply into any technicalities,” Greene said.
The prize will be presented at the 2023 Joint Mathematics Meetings in Boston on Jan. 4.
“The award was a happy corollary; I don’t think that awards should ever be a driving motivation,” Greene said. “ … I do hope the publicity will pique others’ interest in the area I wrote about, which was a joy to share.”