## Update from the Division of Mathematical Sciences

##### *Michael Vogelius, DMS Director; Tie Luo, DMS Deputy Director; and Henry Warchall, DMS Senior Advisor*

With this article, the management team of the Division of Mathematical Sciences (DMS) at the National Science Foundation would like to provide an update about recent program activities from DMS and an outlook for the future. DMS plays a critical role in providing about 64 percent of all U.S. federal support for basic research at the frontiers of discovery in the mathematical sciences. DMS also supports training through research involvement of the next generation of mathematical scientists, conferences and workshops, and a portfolio of national mathematical sciences research institutes.

Here we call attention to four recent funding opportunities we find particularly newsworthy. Two are calls for development of large-scale interdisciplinary research centers/institutes that involve collaboration between mathematical scientists and researchers from other scientific areas, and two are calls for activities to enhance and broaden graduate education in the mathematical sciences.

**Transdisciplinary Research in Principles of Data Science**

The Transdisciplinary Research in Principles of Data Science (TRIPODS) program aims to bring together the statistics, mathematics, and theoretical computer science communities to develop the theoretical foundations of data science through integrated research and training activities. Phase I will support the development of small collaborative institutes. Phase II (to be described in an anticipated future solicitation, subject to availability of funds) will support a smaller number of larger institutes, via a second competitive proposal process. All TRIPODS institutes will involve significant and integral participation by all three communities.

The TRIPODS program is a part of the NSF initiative “Harnessing Data for 21st-Century Science and Engineering,” one of the “Ten Big Ideas for Future NSF Investments.” The TRIPODS program is co-funded equally by the NSF Division of Computing and Communication Foundations (CCF) and DMS. These investments are augmented by funds from the initiative “Growing Convergent Research at NSF” and the Office of Multidisciplinary Activities of the Mathematical and Physical Sciences Directorate.

It is the hope of DMS that the TRIPODS program will emphasize to academic institutions forming programs in data science that such efforts naturally involve computer scientists, mathematicians, and statisticians. The TRIPODS Phase I proposals are under review, and it is anticipated that up to 12 three-year awards of approximately $500,000 per year will be made.

**NSF-Simons Research Centers for Mathematics of Complex Biological Systems**

The NSF-Simons Research Centers for Mathematics of Complex Biological Systems is a new program that expects to fund centers of five-year duration from a one-time call for proposals.

The program focuses on research to understand emergent properties in biological systems. It welcomes proposals to establish centers at which sustained collaborations are facilitated between mathematical scientists and biologists to develop novel mathematical, computational, and statistical approaches to advance fundamental understanding of how and why emergent properties arise in molecular, cellular, and organismal systems. The program strongly encourages projects aimed at developing predictive frameworks for understanding phenotype.

Projects are expected to include plans for significant effort in cross-disciplinary training of cohorts of future scientists, such as postdoctoral research associates, graduate students, and/or undergraduates from mathematical sciences and the areas of the biological sciences that are the focus of this activity. Each center also is envisaged to conduct convening activities, including short-term and/or long-term visitors’ programs, workshops, and/or outreach activities.

The NSF-Simons Research Centers for Mathematics of Complex Biological Systems program is part of the NSF initiative “Understanding the Rules of Life: Predicting Phenotype,” another of the “Ten Big Ideas for Future NSF Investments.” The program is co-funded equally by the Simons Foundation and NSF, with 30% of the total investment furnished by DMS and 20% furnished by the NSF Directorate for Biological Sciences.

Letters of intent and proposals are due August 10 and September 29, respectively. It is anticipated that three centers devoted to collaboration between mathematicians, statisticians, and biologists will be funded. Each center will be funded for a five-year duration with an annual budget of $2 million.

**Mathematical Sciences Graduate Internships**

By means of this activity, DMS aims to provide opportunities to enrich the training of doctoral students in the mathematical sciences through summer research internships in nonacademic settings. DMS has partnered with the Oak Ridge Institute for Science and Education (ORISE), which is managed by Oak Ridge Associated Universities (ORAU) for the Department of Energy, to establish the Mathematical Sciences Graduate Internships program.

The immediate goal of the program is to arrange and support internships for approximately 40 students annually, primarily at the U.S. National Laboratories. The program is intended to introduce doctoral students in the mathematical sciences to important applications of mathematical or statistical theories outside of academia. The internships are aimed at students who are interested in learning about such applications, regardless of whether they plan to pursue an academic or nonacademic career.

Not only will interns gain experience in the diverse uses of advanced mathematical tools at national laboratories, they will also become aware of the additional skills required for success in employment outside the traditional academic setting. The program is equally intended for students in pure and applied areas. It is planned to continue this collaboration with ORISE in 2018.

**Improving and Supporting the Transition to Graduate School in the Mathematical Sciences**

The NSF Directorate for Education and Human Resources (EHR) and DMS in collaboration invite proposals for projects designed to encourage and prepare U.S. students to pursue and succeed in graduate doctoral study in the mathematical sciences. Particular emphasis is placed on broadening participation of students from under-represented populations, including racial/ethnic groups under-represented in mathematics and statistics, individuals with disabilities, and women.

The activity aims to support projects that are scalable to serve large numbers of students without large increases in cost and that are sustainable, that is, have continued impact without ongoing large influxes of grant funding. Projects are expected to involve mathematical sciences research as part of student training and/or educational research that produces new knowledge to help the community understand for whom and under what circumstances proposed activities are effective in preparing a diverse population of students to be successful in graduate school.

**About These New Initiatives**

DMS considers the first two activities to be parts of the DMS research institutes portfolio, which constitutes approximately 12% of the annual DMS investment. These new opportunities represent the continued evolution of the DMS institute portfolio, which the division aims to keep current, dynamic, and responsive to emerging needs of the mathematical sciences community. Both new programs were developed in close consultation with the communities involved, in particular through workshops that provided insight into current activity in these areas and perceived future needs. Both new programs are centered on an intellectual partnership between the mathematical sciences and another discipline, matched by significant financial investment from the other disciplinary partner. This arrangement reflects the worth of the interdisciplinary activity from a scientific viewpoint, in that it certifies the importance of these activities to both disciplines, and it also greatly leverages DMS investments.

DMS considers the last two activities to be parts of the DMS workforce program portfolio, which constitutes approximately 10% of the annual DMS investment. These new opportunities address two distinct community needs in support of the development of the next generation of mathematical scientists.

First, employment data show the majority of mathematical sciences PhD recipients take employment other than conventional academic tenure-track positions, yet many U.S. graduate programs in the mathematical sciences do not provide students with needed information about potential nonacademic career paths. The Mathematical Sciences Graduate Internships program is an early step toward raising doctoral students’ awareness of potential rewarding nonacademic careers.

Second, despite substantial efforts by the mathematical sciences community and investment by funding agencies, current data indicate both the percentage of women and percentage of students from under-represented groups entering doctoral programs and receiving doctoral degrees in the mathematical sciences have remained relatively constant since 2004, and these levels are well below the representation of these groups in the general population. The activity in Improving and Supporting the Transition to Graduate School in the Mathematical Sciences aims to catalyze cost-effective community projects based on proven techniques to address this under-representation.

**Outlook for the Future**

The congressional appropriation for the fiscal year 2017 budget had not been finalized. The expected fiscal year 2017 budget for DMS is $233,512,000, which represents a small decrease of approximately $400,000 from the 2016 level. The president’s fiscal year 2018 budget request to Congress for the NSF will result in a decrease in the DMS budget of approximately $24,000,000, roughly a 10% reduction. The highest priorities for DMS in this challenging budgetary climate are to maintain, to the extent possible, investments in its core activities, namely the disciplinary programs that fund unsolicited proposals for research by individual investigators and the research institutes portfolio.

Looking further into the future, the Mathematical Sciences Research Institutes program will hold an open competition [in fiscal year 2019]. Proposals are invited for new institute projects from U.S. sites, as well as renewal proposals from any of the currently supported U.S.-based Mathematical Sciences Research Institutes. Awards from this competition are anticipated to begin in fiscal year 2020. DMS is committed to maintaining investment in its research institutes portfolio at a level of 12–14% of the total DMS investment over the long term.

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