Mathematics of Information

Information, broadly defined, plays an ever increasingly large role in our scientific and technological endeavors, as well as our daily lives. Collectively, we search the web over billions of times per day, we keep our medical records in digital repositories, we share videos and photos over the web, and we listen to music on MP3 players. Our ability to collect, store, and generate vast quantities of data far outstrips our ability to analyze, process, and understand these data. Many scientific, engineering, and medical applications depend on our ability to handle enormous amounts of complex information. Network engineering involves massive datasets at high speeds, medical imaging generates large data with intricate geometric relationships, and astronomical observations include data at different wavelengths or spectral bands.

Our current technology and scientific tools for information lag far behind our ability to collect enormous amounts of data, our need to analyze that data as efficiently as possible, and, finally, our ability to use that analysis to make sound, timely decisions. The gap between our tools and the volume of data we collect will increase unless we undertake a significant effort to improve these tools. Concomitantly, unless we have a clear picture of how we will use the information we extract, tools to do so will be useless. This gap widens at a time when it is increasingly critical for homeland security, Internet security, technical and biological insight that we analyze information quickly and that we derive meaningful information from it efficiently. In addition, whatever ad hoc tools we develop in the course of handling these volumes of information, it is imperative that we gain a rigorous understanding of the capabilities, advantages, and pitfalls in these methods so that we understand their limitations and gain insight in how to mitigate them.

The Mathematics of Information program will involve invited long-term visitors, New Direction Visiting Professors, as well as postdoctoral fellows. Six workshops on rapidly growing research areas are being organized. In addition, there will be tutorials as well as short courses offered to introduce graduate students, postdocs, and other researchers in neighboring areas to the topics covered in the workshops. Each workshop is designed to be truly interdisciplinary, involving researchers from mathematical sciences, computer sciences, engineering, and other fields.