EMSW21-RTG: Enhancing the Research Workforce in Algebraic Geometry and its Boundaries in the Twenty-First Century

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The project establishes a research training program in algebraic geometryand its boundary areas at the University of Michigan. Target trainees arerecent PhDs and advanced graduate students. The project is run by fivesenior faculty members representing a wide swath of current researchtrends in algebraic geometry, in consultation with an additional 14 seniorfaculty at Michigan in related areas. Activities include innovations inseminar structure offering trainees broad exposure to a wide variety ofbasic 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 prominentresearcher from outside Michigan; opportunities for post-doctoralresearchers to design and lead REU projects under the mentorship of asenior faculty member; opportunities for advanced graduate students andpost-docs to develop their technical lecturing and writing skills; andnumerous opportunities for post-docs and advanced graduate students toreceive mentoring on all aspects of a research career in mathematics.Algebraic geometry is one of the most central and active branches ofmathematics today, with increasingly important connections to otherbranches of mathematics and science. Algebraic geometry also underliesmany applications of mathematics to technology and government, includingcoding theory (bringing us, for example, the compact disc) and splinetheory (bringing us computer aided design and the computer graphicsessential to certain medical applications and Hollywood movies), as wellas important issues of national security pioneered by the NationalSecurity Agency. The explosive growth of algebraic geometry at the end ofthe twentieth century has made this a very exciting time to begin researchin the field, but it has also made it difficult for young researchers toget started. This project will increase the flow of broadly trainedresearchers in algebraic geometry and its boundary areas, thereforeenhancing the training infrastructure and the research workforce in thesevital areas of mathematics in the twenty-first century.