Gunnar E. Carlsson | |
|---|---|
 | |
| Born | (1952-08-22)22 August 1952 (age 72) Stockholm, Sweden |
| Nationality | American |
| Alma mater | Stanford University Harvard University |
| Known for | Segal conjecture Topological data analysis |
| Awards | Alfred P. Sloan fellow |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Stanford University University of Chicago University of California, San Diego Princeton University |
| Doctoral advisor | R. James (Richard) Milgram |
| Doctoral students | |
Gunnar E. Carlsson (born August 22, 1952 inStockholm,Sweden) is an Americanmathematician, working inalgebraic topology. He is known for his work on theSegal conjecture, and for his work on applied algebraic topology, especiallytopological data analysis. He is a Professor Emeritus in the Department of Mathematics atStanford University.[1] He is the founder and president of the predictive technology company Ayasdi.[2]
Carlsson was born inSweden and was educated in theUnited States. He graduated fromRedwood High School (Larkspur, California) in 1969. He received a Ph.D. fromStanford University in 1976, with a dissertation written under the supervision ofR. J. Milgram. He was a Dickson Assistant Professor at theUniversity of Chicago (1976-1978) and Professor at theUniversity of California, San Diego (1978–86),Princeton University (1986-1991), andStanford University (1991–2015) where he held the Anne and Bill Swindells Professorship and was Chair of the Department of Mathematics from 1995 to 1998.[1]
He was an Ordway Visiting Professor at theUniversity of Minnesota (May–June 1991) and held aSloan Foundation Research Fellowship (1984-1986).[1] He has delivered aninvited address at the International Congress of Mathematicians in Berkeley, California, in 1986;[3] a plenary address at the annual meeting of theAmerican Mathematical Society (1984);[4] theWhittaker Colloquium at theUniversity of Edinburgh (2011);[5] the Rademacher Lectures at theUniversity of Pennsylvania (2011);[6] and an invited plenary address at the annual meeting of the Society of Industrial and Applied Mathematics (2012).[7]He was elected as a member of the 2017 class of Fellows of theAmerican Mathematical Society "for contributions to algebraic topology, particularly equivariant stable homotopy theory, algebraic K-theory, and applied algebraic topology".[8]
In 2008, Carlsson cofounded Ayasdi, a predictive technology based on big data, machine learning and artificial intelligence.[9]
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Segal's Burnside conjecture provides a description of the stablecohomotopy theory of theclassifying space of afinite group. It is the analogue for cohomotopy of the work ofMichael Atiyah andGraeme Segal on theK-theory of these classifying spaces. Building on earlier work byFrank Adams,Jeremy Gunawardena,Haynes Miller,J. Peter May, James McClure, and L. Gaunce Lewis, Carlsson proved this conjecture in 1982. He also adapted the techniques to provide a proof ofSullivan's fixed point conjecture, which was also proved simultaneously and independently by Miller andJean Lannes.
Algebraic K-theory is atopological construction that assignsspaces (ultimatelyspectra) torings,schemes, and other non-topological input. It has connections with important questions in high-dimensionaltopology, notably the conjectures ofNovikov andBorel. Carlsson has proved, jointly with E. Pedersen and B. Goldfarb Novikov's conjecture for large classes of groups.
Carlsson has worked incomputational topology, especially as it applies to theanalysis of high dimensional and complex data sets. In collaboration with others, he has demonstrated the utility of bothpersistent homology and the Mapper methodology in a series of papers. This work is central to the development of tools by Ayasdi, Inc, for analyzing massive and complex data sets across multiple application domains. In January 2016, he published a topological data analysis on theDonald Trump presidential campaign, 2016 and was able to outline the reach potential of Trump's messages in the mind of skeptical voters.[10]
Carlsson is married and has three children.[2]
