MPS Mathematical Sciences

**Mathematical sciences programs** MPS invests in multiple mathematical sciences programs supporting disciplinary and interdisciplinary research, individual researchers and groups, and education and training opportunities for students. * * * **[Algebra and Number Theory](https://www.nsf.gov/funding/opportunities/algebra-number-theory "Algebra and Number Theory")** Supports research in algebra, algebraic and arithmetic geometry, number theory and representation theory. **[Analysis](https://www.nsf.gov/funding/opportunities/analysis "Analysis")** Supports research in complex, harmonic and real analysis; dynamical systems and ergodic theory; functional analysis; mathematical physics; operator theory and operator algebras; partial differential equations and calculus of variations. **[Applied Mathematics](https://www.nsf.gov/funding/opportunities/applied-mathematics "Applied Mathematics")** Supports mathematics research motivated by or affecting problems arising in science and engineering. **[Combinatorics](https://www.nsf.gov/funding/opportunities/combinatorics "Combinatorics")** Supports research on discrete structures. Focus areas include algebraic and geometric combinatorics, probabilistic and structural graph theory. **[Computational Mathematics](https://www.nsf.gov/funding/opportunities/computational-mathematics "Computational Mathematics")** Supports the development and analysis of innovative approaches to address the broad range of mathematical questions and challenges that arise from the implementation of numerical algorithms. **[Foundations](https://www.nsf.gov/funding/opportunities/foundations "Foundations")** Supports research in mathematical logic and the foundations of mathematics, including proof theory, recursion theory, model theory, set theory and infinitary combinatorics. **[Geometric Analysis](https://www.nsf.gov/funding/opportunities/geometric-analysis "Geometric Analysis")** Supports research in differential geometry, geometric partial differential equations, geometric methods in modern mathematical physics, geometry of convex sets, integral geometry and related geometric topics. **[Mathematical Biology](https://www.nsf.gov/funding/opportunities/mathematical-biology "Mathematical Biology")** Supports research in all areas of applied and computational mathematical sciences relevant to the biological and life sciences. **[Mathematical Sciences Focused Research Groups](https://www.nsf.gov/funding/opportunities/frgms-focused-research-groups-mathematical-sciences "Focused Research Groups in the Mathematical Sciences (FRGMS)")** Supports collaborative groups employing innovative methods to solve specific, major research challenges in the mathematical sciences. **[Mathematical Sciences Research Infrastructure](https://www.nsf.gov/funding/opportunities/mathematical-sciences-infrastructure-program "Mathematical Sciences Infrastructure Program")** Supports efforts to strengthen research infrastructure across the mathematical sciences community and training projects that complement existing opportunities. **[Mathematical Sciences Research Training Groups](https://www.nsf.gov/funding/opportunities/rtg-research-training-groups-mathematical-sciences "Research Training Groups in the Mathematical Sciences (RTG)")** Supports efforts to improve graduate student research training and professional development in all areas of the mathematical sciences. **[Probability](https://www.nsf.gov/funding/opportunities/probability "Probability")** Supports research on the theory and applications of probability including discrete probability, stochastic processes, limit theory, interacting particle systems, stochastic differential and partial differential equations and Markov processes. **[Statistics](https://www.nsf.gov/funding/opportunities/statistics "Statistics")** Supports research in statistical theory and methods, including research in statistical methods with applications in any domain of science and engineering. **[Topology](https://www.nsf.gov/funding/opportunities/topology "Topology")** Supports research on algebraic topology, differential topology, geometric group theory and low dimensional topology.