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Gunnar E. Carlsson (born August 22, 1952 in
Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...
,
Sweden Sweden, formally the Kingdom of Sweden, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, and Finland to the east. At , Sweden is the largest Nordic count ...
) is an American
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
, working in
algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...
. He is known for his work on the Segal conjecture, and for his work on applied algebraic topology, especially
topological data analysis In applied mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA ...
. He is a Professor Emeritus in the Department of Mathematics at
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
. He is the founder and president of the predictive technology company Ayasdi.


Biography

Carlsson was born in
Sweden Sweden, formally the Kingdom of Sweden, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. It borders Norway to the west and north, and Finland to the east. At , Sweden is the largest Nordic count ...
and was educated in the
United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
. He graduated from Redwood High School (Larkspur, California) in 1969. He received a Ph.D. from
Stanford Leland Stanford Junior University, commonly referred to as Stanford University, is a private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth governor of and th ...
University in 1976, with a dissertation written under the supervision of R. J. Milgram. He was a Dickson Assistant Professor at the
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
(1976-1978) and Professor at the
University of California, San Diego The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Es ...
(1978–86),
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
(1986-1991), and
Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...
(1991–2015) where he held the Anne and Bill Swindells Professorship and was Chair of the Department of Mathematics from 1995 to 1998. He was an Ordway Visiting Professor at the
University of Minnesota The University of Minnesota Twin Cities (historically known as University of Minnesota) is a public university, public Land-grant university, land-grant research university in the Minneapolis–Saint Paul, Twin Cities of Minneapolis and Saint ...
(May–June 1991) and held a
Sloan Foundation The Alfred P. Sloan Foundation is an American philanthropic nonprofit organization. It was established in 1934 by Alfred P. Sloan Jr., president and chief executive officer of General Motors. The Sloan Foundation makes grants to support origin ...
Research Fellowship (1984-1986). He has delivered an invited address at the International Congress of Mathematicians in Berkeley, California, in 1986; a plenary address at the annual meeting of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
(1984); the Whittaker Colloquium at the
University of Edinburgh The University of Edinburgh (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...
(2011); the Rademacher Lectures at the
University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...
(2011); and an invited plenary address at the annual meeting of the Society of Industrial and Applied Mathematics (2012). He was elected as a member of the 2017 class of Fellows of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
"for contributions to algebraic topology, particularly equivariant stable homotopy theory, algebraic K-theory, and applied algebraic topology". In 2008, Carlsson cofounded Ayasdi, a predictive technology based on big data, machine learning and artificial intelligence.


Work


Equivariant methods in homotopy theory

Segal's Burnside conjecture provides a description of the stable cohomotopy theory of the
classifying space In mathematics, specifically in homotopy theory, a classifying space ''BG'' of a topological group ''G'' is the quotient of a weakly contractible space ''EG'' (i.e., a topological space all of whose homotopy groups are trivial) by a proper free ...
of a
finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...
. It is the analogue for cohomotopy of the work of
Michael Atiyah Sir Michael Francis Atiyah (; 22 April 1929 – 11 January 2019) was a British-Lebanese mathematician specialising in geometry. His contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the ...
and Graeme Segal on the
K-theory In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is a cohomology theory known as topological K-theory. In algebra and algebraic geometr ...
of these classifying spaces. Building on earlier work by
Frank Adams John Frank Adams (5 November 1930 – 7 January 1989) was a British mathematician, one of the major contributors to homotopy theory. Life He was born in Woolwich, a suburb in south-east London, and attended Bedford School. He had a younger br ...
, 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 of Sullivan's fixed point conjecture, which was also proved simultaneously and independently by Miller and
Jean Lannes Jean Lannes, 1st Duke of Montebello, Prince of Siewierz (; 10 April 1769 – 31 May 1809), was a French military commander and a Marshal of the Empire who served during both the French Revolutionary and Napoleonic Wars. He was one of Napol ...
.


Algebraic K-theory

Algebraic K-theory Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sens ...
is a
topological Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, wit ...
construction that assigns
space Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless ...
s (ultimately spectra) to
ring (The) Ring(s) may refer to: * Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry * To make a sound with a bell, and the sound made by a bell Arts, entertainment, and media Film and TV * ''The Ring'' (franchise), a ...
s, schemes, and other non-topological input. It has connections with important questions in high-dimensional
topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
, notably the conjectures of Novikov and
Borel Borel may refer to: People * Antoine Borel (1840–1915), a Swiss-born American businessman * Armand Borel (1923–2003), a Swiss mathematician * Borel (author), 18th-century French playwright * Borel (1906–1967), pseudonym of the French actor ...
. Carlsson has proved, jointly with E. Pedersen and B. Goldfarb Novikov's conjecture for large classes of groups.


Applied and computational topology

Carlsson has worked in
computational topology Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its ...
, especially as it applies to the
analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
of high dimensional and complex data sets. In collaboration with others, he has demonstrated the utility of both
persistent homology In topological data analysis, persistent homology is a method for computing topological features of a space at different spatial resolutions. More persistent features are detected over a wide range of spatial scales and are deemed more likely to ...
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 the
Donald Trump presidential campaign, 2016 Donald Trump ran a successful campaign for the 2016 United States presidential election, 2016 U.S. presidential election. He formally announced his campaign on June 16, 2015, at Trump Tower in New York City, initially battling for the 2016 ...
and was able to outline the reach potential of Trump's messages in the mind of skeptical voters.


Private life

Carlsson is married and has three children.


References

{{DEFAULTSORT:Carlsson, Gunnar 1952 births Living people 20th-century American mathematicians 21st-century American mathematicians Fellows of the American Mathematical Society Harvard University alumni Redwood High School (Larkspur, California) alumni Stanford University Department of Mathematics faculty Stanford University School of Humanities and Sciences alumni Swedish emigrants to the United States Topologists University of Chicago faculty Academics from Stockholm