Special Meeting: Foundations of Computational Mathematics

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This thematic program will explore the evolving interface between mathematics and computation. A wide variety of mathematical disciplines are involved, including computational algebraic geometry and symbolic computation, computational number theory, computational geometry, topology and dynamics, complexity and computability in real computation, computer science and optimization theory. Algorithms will be central, not only in their traditional role in the invention and analysis of numerical methods, but also as fundamental theoretical tools for mathematical experimentation and discovery, as proof techniques, and as models of computability and tractability. By assembling a large, broad group of participants, ranging from established mathematicians and computer scientists to graduate students, the program will transform our knowledge of computational mathematics well into the future.The Fields Institute in Toronto will host this timely six-month program, capitalizing on rapidly evolving networks of international expertise linking mathematics and computation; NSF funding will support participation of junior U.S. researchers and graduate students. The impact of constantly increasing computational power on applied mathematics, science and engineering, motivated by new applications such as encryption, data mining, and web search, has inevitably led to the study of the computational tools themselves, creating and reinvigorating a rich spectrum of mathematical disciplines broadly represented at this special semester. The program involves three one-week focus workshops, special lecture series and graduate courses (delivered in particular by two distinguished U.S. female computer scientists, Eva Tardos and Lenore Blum), diverse senior and junior researchers and postdoctoral fellows making long- and short-term visits and engaging in day-to-day interaction, and extensive efforts to disseminate the emerging new science. These diverse activities will integrate cutting-edge research, interdisciplinary synergy, and learning and training opportunities for an array of participants as broad and inclusive as possible.