# Karl Löwner and His Student Lipman Bers—Pre-war Prague Mathematicians

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*Martina Bečvářová; Ivan Netuka*

A publication of the European Mathematical Society

This monograph is devoted to two distinguished mathematicians,
Karl Löwner (1893–1968) and Lipman Bers (1914–1993),
whose lives are dramatically interlinked with key historical events of
the 20th century. Karl Löwner, Professor of Mathematics at the
German University in Prague (Czechoslovakia), was dismissed from his
position because he was a Jew, and emigrated to the USA in 1939 (where
he changed his name to Charles Loewner). Earlier, he had published
several outstanding papers in complex analysis and a masterpiece on
matrix functions. In particular, his groundbreaking parametric method
in geometric function theory from 1923, which led to Löwner's
celebrated differential equation, brought him worldwide fame and
turned out to be a cornerstone in de Branges' proof of the Bieberbach
conjecture.

Unexpectedly, Löwner's differential equation has gained recent
prominence with the introduction of a conformally invariant stochastic
process called stochastic Loewner evolution (SLE) by O. Schramm in
2000. SLE features in two Fields Medal citations from 2006 and
2010. Lipman Bers was the final Prague Ph.D. student of
Löwner. His dissertation on potential theory (1938), completed
shortly before his emigration and long thought to be irretrievably
lost, was found in 2006. It is made accessible here for the first
time, with an extensive commentary, to the mathematical community.

This monograph presents an in-depth account of the lives of both
mathematicians, with special emphasis on the pre-war period. Löwner's
teaching activities and professional achievements are presented in the
context of the prevailing complex political situation and against the
background of the wider development of mathematics in Europe. Each of
his publications is accompanied by an extensive commentary, tracing the
origin and motivation of the problem studied, and describing the
state-of-art at the time of the corresponding mathematical field.
Special attention is paid to the impact of the results obtained and to
the later development of the underlying ideas, thus connecting Löwner's
achievements to current research activity. The text is based on an
extensive archival search, and most of the archival findings appear here
for the first time.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Anyone with an interest in the history of mathematics.