Lars V. Ahlfors was a mathematician whose major area of research was complex analysis. In 1936, he was one of the first to receive a Fields Medal. Often considered the equivalent of the Nobel Prize, the Fields Medal is given every four years to a mathematician under the age of forty who has achieved important results in his or her work. Ahlfors received this award for his work on Riemann surfaces, which are schematic devices for mapping the relation between complex numbers according to an analytic function. Ahlfors's results led to new developments in the field of meromorphic functions (functions that are analytic everywhere in a region except for a finite number of poles); the methods he developed to obtain these results created an entirely new field of analysis.
Lars Valerian Ahlfors was born on April 18, 1907 in Helsingfors (now Helsinki), Finland. His mother, Sievä Helander Ahlfors, died giving birth to him. His father, Axel Ahlfors, was a mechanical engineering professor at the Polytechnical Institute. Even as a child, Ahlfors was interested in mathematics; his high school did not offer calculus courses, but Ahlfors taught himself by reading his father's engineering books.
He did not have access to mathematical books until he began his studies in 1924 at the University of Helsingfors, where he was taught by Ernst Lindelöf and Rolf Nevanlinna . Lindelöf worked in complex analysis and was known as the father of mathematics in Finland--mostly because, in the 1920s, all Finnish mathematicians were his students. Ahlfors received his degree in the spring of 1928, and he also began his graduate work that year. Although there were no official graduate courses in mathematics at the university, Lindelöf supervised students' advanced readings.
Ahlfors took his first official graduate course in mathematics in the fall of 1928, when he accompanied Nevanlinna to Zürich. The class Nevanlinna taught was on contemporary function theory. Topics included the major parts of Nevanlinna's theory of meromorphic functions and Denjoy's conjecture on the number of asymptotic values of an entire function,as well as Carleman's partial proof of it. During his study of this subject, Ahlfors proved the full Denjoy conjecture after he discovered a new approach based on conformal mapping. A conformal map is a function in which, if two curves intersect at an angle, then the images of the curves in the map will also intersect at the same angle.
When the course ended, Ahlfors travelled to Paris, where he continued his work for three months before returning to Finland. His research there led to a geometric interpretation of the Nevanlinna theory, which he would publish in 1935. Although this interpretation was also discovered independently in Japan, it was the beginning of Ahlfors's concentration on meromorphic functions.
When he returned to Finland, Ahlfors was given the position of lecturer at Åbo Akademi, Finland's Swedish-language university. He also began work on his thesis, the subject of which was conformal mapping and entire functions. He had finished his thesis by the spring of 1930, and received his Ph.D. in 1932. Ahlfors was named a fellow of the Rockefeller Institute in 1932, which allowed him to live and do research in Paris for a year. In July of 1933, he married Erna Lehnert; they would have three daughters. He returned to the University of Helsingfors that same year as an adjunct professor and taught there until the fall of 1935, when he began a three-year assignment as assistant professor at Harvard University.
For his research in Riemann surfaces of inverse functions in terms of covering surfaces, Ahlfors was awarded the Fields Medal by the International Congress of Mathematicians in 1936. Ahlfors was attending the ceremony in Oslo, but he learned only hours before it began that he had been chosen as the recipient. In the talk about Ahlfors's work he gave to the congress, German mathematician Constantin Carathéodory specifically noted the contribution of Ahlfors's paper, "On the Theory of Covering Surfaces," which explained the methods Ahlfors had developed in his work on Riemann surfaces. Carathéodory pointed out that these methods were also the start of a new branch of analysis, which he termed "metrical topology."
In the spring of 1938, Ahlfors left the United States and returned to Finland to take a position as a professor at the University of Helsinki. World War II soon spread to Finland, however, and the university closed because there were not enough students. Although his family was evacuated to Sweden, Ahlfors stayed in Helsinki. He was not called for military duty because of a physical condition, but he participated in the military's communications setup.
In the summer of 1944, the University of Zürich offered Ahlfors a professorship, and he accepted the position. After an arduous journey from Sweden to Switzerland because of the war, he began teaching in the summer of 1945. He was not happy there, however, so when Harvard University asked him to return he gladly accepted. He began teaching there in the fall of 1946 and became a naturalized United States citizen in 1952. In 1953, Ahlfors's book Complex Analysis was published. It is still widely used as a basic text in graduate courses. In 1964, he was named William Caspar Graustein Professor of Mathematics. Ahlfors remained at Harvard until his retirement as Professor Emeritus in 1977, subsequently moving to Boston. He died in Pittsfield, Massachusetts.
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