Per Enflo facts for kids

Quick facts for kids Per Enflo
Enflo in 1972
Born	(1944-05-20) 20 May 1944 (age 79) Stockholm, Sweden
Alma mater	Stockholm University
Known for	Approximation problem Schauder basis Hilbert's fifth problem (infinite-dimensional) uniformly convex renorms of super-reflexive Banach spaces embedding metric spaces (unbounded distortion of cube) "Concentration" of polynomials at low degree Invariant subspace problem
Awards	Mazur's "live goose" for solving "Scottish Book" Problem 153
Scientific career
Fields	Functional analysis Operator theory Analytic number theory
Institutions	University of California, Berkeley Stanford University École Polytechnique, Paris The Royal Institute of Technology, Stockholm Kent State University
Doctoral advisor	Hans Rådström
Doctoral students	Angela Spalsbury Bruce Reznick

Per H. Enflo (Swedish: [ˈpæːr ˈěːnfluː]; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved problems that had been considered fundamental. Three of these problems had been open for more than forty years:

• The basis problem and the approximation problem and later
• the invariant subspace problem for Banach spaces.

In solving these problems, Enflo developed new techniques which were then used by other researchers in functional analysis and operator theory for years. Some of Enflo's research has been important also in other mathematical fields, such as number theory, and in computer science, especially computer algebra and approximation algorithms.

Enflo works at Kent State University, where he holds the title of University Professor. Enflo has earlier held positions at the Miller Institute for Basic Research in Science at the University of California, Berkeley, Stanford University, École Polytechnique, (Paris) and The Royal Institute of Technology, Stockholm.

Enflo is also a concert pianist.

Mathematical biology: Population dynamics

In applied mathematics, Per Enflo has published several papers in mathematical biology, specifically in population dynamics.

Human evolution

Enflo has also published in population genetics and paleoanthropology.

Today, all humans belong to one population of Homo sapiens sapiens, which is individed by species barrier. However, according to the "Out of Africa" model this is not the first species of hominids: the first species of genus Homo, Homo habilis, evolved in East Africa at least 2 Ma, and members of this species populated different parts of Africa in a relatively short time. Homo erectus evolved more than 1.8 Ma, and by 1.5 Ma had spread throughout the Old World.

Anthropologists have been divided as to whether current human population evolved as one interconnected population (as postulated by the Multiregional Evolution hypothesis), or evolved only in East Africa, speciated, and then migrating out of Africa and replaced human populations in Eurasia (called the "Out of Africa" Model or the "Complete Replacement" Model).

Neanderthals and modern humans coexisted in Europe for several thousand years, but the duration of this period is uncertain. Modern humans may have first migrated to Europe 40–43,000 years ago. Neanderthals may have lived as recently as 24,000 years ago in refugia on the south coast of the Iberian peninsula such as Gorham's Cave. Inter-stratification of Neanderthal and modern human remains has been suggested, but is disputed.

With Hawks and Wolpoff, Enflo published an explanation of fossil evidence on the DNA of Neanderthal and modern humans. This article tries to resolve a debate in the evolution of modern humans between theories suggesting either multiregional and single African origins. In particular, the extinction of Neanderthals could have happened due to waves of modern humans entered Europe – in technical terms, due to "the continuous influx of modern human DNA into the Neandertal gene pool."

Enflo has also written about the population dynamics of zebra mussels in Lake Erie.

A concert pianist, Per Enflo debuted at the Stockholm Concert Hall in 1963.

Piano

Per Enflo is also a concert pianist.

A child prodigy in both music and mathematics, Enflo won the Swedish competition for young pianists at age 11 in 1956, and he won the same competition in 1961. At age 12, Enflo appeared as a soloist with the Royal Opera Orchestra of Sweden. He debuted in the Stockholm Concert Hall in 1963. Enflo's teachers included Bruno Seidlhofer, Géza Anda, and Gottfried Boon (who himself was a student of Arthur Schnabel).

In 1999 Enflo competed in the first annual Van Cliburn Foundation's International Piano Competition for Outstanding Amateurs .

Enflo performs regularly around Kent and in a Mozart series in Columbus, Ohio (with the Triune Festival Orchestra). His solo piano recitals have appeared on the Classics Network of the radio station WOSU, which is sponsored by Ohio State University.

External sources

• Biography of Per Enflo at Canisius College
• Homepage of Per Enflo at Kent State University

Databases

• Per Enflo at the Mathematics Genealogy Project