The proof of the Mumford conjecture concerning the cohomology of the stable mapping class group serves as a primary benchmark for the career of Danish mathematician Ib Madsen. Collaborating with Michael Weiss, Madsen established a foundational result in algebraic topology, reshaping the understanding of moduli spaces within the field of pure mathematics.
Academic Formation and Early Career
Madsen completed his initial studies at the University of Copenhagen in 1965. He subsequently relocated to pursue doctoral research at the University of Chicago, where he concluded his PhD in 1970 under the supervision of J. Peter May. He maintained this position for thirty-seven years, contributing to the institution until 2008.
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The development of topological cyclic homology theory stands alongside his work on the Mumford conjecture as a significant contribution to topology. His research often involves collaborative efforts with colleagues, resulting in notable publications in journals such as the Annals of Mathematics and Acta Mathematica. Throughout his tenure, he has mentored numerous doctoral students, including Søren Galatius and Lars Hesselholt, who have carried forward his focus on algebraic structures.
Professional Appointments and Recognition
After departing Aarhus University in 2008, Madsen joined the University of Copenhagen, where he continued his academic work until 2016. His professional impact earned him admission to several prestigious organizations, including the Royal Danish Academy of Sciences and Letters in 1978 and the Royal Swedish Academy of Sciences in 1998. In 2011, he received the Ostrowski Prize for his contributions to pure mathematics, sharing the honor with Kannan Soundararajan and David Preiss. He also became a fellow of the American Mathematical Society in 2013.
Fast facts
- Born: 1942, Copenhagen
- Citizenship: Kingdom of Denmark
- PhD Advisor: J. Peter May
- Primary Affiliation: Aarhus University (1971-2008)
- Ostrowski Prize: 2011
- Fellow of the American Mathematical Society: 2013
- Languages: English, Danish
Questions readers ask
What is Ib Madsen most known for in mathematics?
He is recognized for proving the Mumford conjecture on the cohomology of the stable mapping class group alongside Michael Weiss, as well as developing topological cyclic homology theory.
Where did Ib Madsen hold academic faculty positions?
He served on the faculty at Aarhus University from 1971 to 2008 and at the University of Copenhagen from 2008 to 2016.
Achievements
- Ostrowski Prize — 2011
- Held posts at University of Copenhagen and Aarhus University
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