The project establishes a research training program in algebraic geometry and its boundary areas at the University of Michigan. Target trainees are recent PhDs and advanced graduate students. The project is run by five senior faculty members representing a wide swath of current research trends in algebraic geometry, in consultation with an additional 14 senior faculty at Michigan in related areas. Activities include innovations in seminar structure offering trainees broad exposure to a wide variety of basic and research level topics in algebraic geometry (broadly construed); an annual school (open also to young researchers outside Michigan) covering a research topic of current importance taught by a prominent researcher from outside Michigan; opportunities for post-doctoral researchers to design and lead REU projects under the mentorship of a senior faculty member; opportunities for advanced graduate students and post-docs to develop their technical lecturing and writing skills; and numerous opportunities for post-docs and advanced graduate students to receive mentoring on all aspects of a research career in mathematics.
Algebraic geometry is one of the most central and active branches of mathematics today, with increasingly important connections to other branches of mathematics and science. Algebraic geometry also underlies many applications of mathematics to technology and government, including coding theory (bringing us, for example, the compact disc) and spline theory (bringing us computer aided design and the computer graphics essential to certain medical applications and Hollywood movies), as well as important issues of national security pioneered by the National Security Agency. The explosive growth of algebraic geometry at the end of the twentieth century has made this a very exciting time to begin research in the field, but it has also made it difficult for young researchers to get started. This project will increase the flow of broadly trained researchers in algebraic geometry and its boundary areas, therefore enhancing the training infrastructure and the research workforce in these vital areas of mathematics in the twenty-first century.
