David Bindel, Associate Professor of Computer Science, has been appointed the Director of Cornell’s Center for Applied Mathematics (CAM) with a tenure to run from July 1, 2020 to June 30 2025. CS News reached out to Bindel for some historical context on the Center as well details about his work with students, research collaborations with colleagues, and his sense of the Center’s vital role during the ongoing coronavirus pandemic.
Cornell has a long history in applied mathematics: indeed, the first Ph.D. offered by Cornell University—to Henry Turner Eddy in 1872—was in applied mathematics. Eddy’s previous training was in civil engineering, so our tradition of seeing applied mathematics as an area that spans disciplines also goes back a long way.
The Center for Applied Mathematics (CAM) was created in 1964 “to encourage the application of mathematical knowledge in the physical, biological, and social sciences.” The first director was Bill Sears, an aerodynamicist educated under Theodore von Kármán at Caltech, who was returning to academia after time spent in industry at Northrup. The center started with twenty members from math, engineering, physics, and chemistry. Today, we have over a hundred members, from an even broader array of disciplines, but still are guided by that original mission of encouraging the application of mathematical knowledge across a wide range of disciplines.
On a pertinent side note, Bill Sears went on a brief administrative leave almost immediately after arriving at Cornell, and Anil Nerode stepped in as the acting director of CAM for 1964-65. That put Nerode on the committee that worked to start the Computer Science department. So, the connection between CAM and CS goes back to the very beginning of both units.
2. Center for Applied Mathematics (CAM)
CAM today is a center of several applied math activities on campus. The core of the Center is the graduate field of applied mathematics, which has over one hundred affiliated faculty and included forty-seven Ph.D. majors during the 2019-20 academic year. We also have a postdoctoral program meant to foster interdisciplinary applied math collaborations across campus, and a colloquium series that brings a wide variety of applied mathematicians to campus. The physical heart of the program is a space on the sixth floor of Rhodes Hall where all of our Ph.D. students and postdocs have their desks.
The structure of the applied math graduate field is very flexible; research can be essentially about whatever catches a student’s interest, so long as it involves the creative application of advanced mathematics. In addition to a committee chair in applied mathematics, students in CAM are required to have a minor in mathematics and a minor in some other field, with representatives of those fields on their committee. Because applied math is an “orphan" graduate field without an associated department, the faculty affiliated with applied math have a wide range of departmental homes; and our Ph.D. students are integrated with exciting initiatives across campus in biology, engineering, computing, finance, and more. Of the forty-seven current CAM students, twenty-five are advised by faculty in the College of Engineering (COE) and Computing and Information Science (CIS). And of those in CIS, nine are advised by Computer Science faculty.
3. Bindel’s Work with CAM students
I’ve advised six CAM students, including three current Ph.D.s and three graduates (all now working in industry as data scientists or research scientists—since the skills that CAM students learn are very broadly applicable). They’ve worked on a variety of problems, including network analysis, methods for optimization of large-scale engineering problems, optimal design of magnetic fields used in experimental nuclear fusion devices, and design and simulation of large-amplitude waves in micro-electro-mechanical systems (MEMS). I’m also pleased to be on the committee for seven other current applied math Ph.D. students working on an even wider range of problems.
4. Bindel’s Plans for CAM during the Pandemic
Part of the role of CAM is in sparking interdisciplinary collaborations around applied mathematics, and I plan to continue to look for those opportunities. In particular, it’s an exciting time for those of us working at the interface between traditional computational modeling and new methods that exploit modern advances in machine learning. I have been involved in several proposal efforts recently to try to apply AI and ML methods to big problems in physics, chemistry, and engineering. I think this is the type of effort where CAM has played a very strong role in the past and will continue to play a critical role going forward.
The current pandemic has also highlighted the importance of mathematical modeling in ways that would have been difficult to imagine a year ago. Suddenly the popular media is full of explanations of exponentials and S-curves and standard differential equations (SIR models) describing epidemics, not to mention discussions of modeling uncertainties and the role of models in determining policies. At the start of the calendar year, Alex Vladimirsky (the current and outgoing CAM director) and I sent a proposal to the National Science Foundation (NSF) for a large training grant for “Math Modeling with Policy Implications,” with an emphasis on mathematical modeling for understanding how different policies might affect the future of work. What seemed important to us then seems like it should be even more obviously important to the world now, and the close ties between applied math and the social sciences, along with growing ties to Industrial and Labor Relations (ILR), help make Cornell uniquely well-qualified to do this type of work.
In addition to highlighting the importance of mathematical modeling to informing policy, the current crisis has made it evident how important it is that we are able to convey the meaning of these models to policy makers and to the general public. A current CAM activity is a seminar run by Steven Strogatz on communicating mathematical ideas across fields and to diverse audiences. This is one of the activities under a current grant for research training at the nexus of dynamics, probability, and PDEs. While this current grant will come to an end in the summer of 2022, we clearly need to continue this type of effort going forward, and this is also one of the proposed efforts in our recently-submitted NSF proposal.