# Josef Hofbauer

I was born in 1956 in
Lower Austria and grew up between
Traismauer (an old
town) and
Nussdorf
ob der Traisen.
My mathematics teacher
**Dr. Hubert Unfried **
at the Piaristengymnasium in
Krems an der Donau nurtured my interest in mathematics, in particular by guiding me to
Mathematical Olympiads.
From 1974 to 1978 I studied mathematics at the University of Vienna and
did my Ph.D. under Prof. Johann Cigler on extensions of the binomial theorem and
umbral calculus.
One of my old combinatorial papers (on
Lagrange Inversion )
has become available on the WWW, thanks to
my colleague
Christian Krattenthaler.

Since 1979 I have been working at the Department of Mathematics of the
University of Vienna, first as assistant and since 1985 as Dozent.
In 1996 I received the title Außerordentlicher Universitätsprofessor.
From 2006 until 2021 I was Professor for Biomathematics at the University of Vienna.

#### Stays outside and abroad

winter term 1980: postdoc at
Peter Schuster's
department
of theoretical chemistry

Summer 1984: YSSP at the International Institute for Applied Systems Analysis (IIASA), Laxenburg

1985/86: visiting professor resp. Erwin-Schrödinger scholar
at
Northwestern University
in Evanston, Illinois (special year on Dynamical Systems)

Fall term 1988: visiting professor at the
University of Alberta
in Edmonton, Canada.

1994/95: Research Fellow at
Collegium Budapest
- Institute for Advanced Study

Spring 2002: visiting professor at the Ecole Polytechnique in Paris

Jan 2004 - Sept 2006: Chair of Mathematical Biology at University College London

Spring 2009: visiting professor at the Ecole Polytechnique in Paris

February 2012: visiting professor at Universite de Pierre et Marie Curie in Paris

Summer 2013: visitor at the Hausdorff Institute in Bonn

February 2015: visitor at SUSTC in Shenzhen, China

### Research

I am mainly interested in
dynamical systems (qualitative theory
of differential equations) and their applications to biomathematics,
in particular population dynamics
(permanence), and evolutionary game theory.

My collaboration with
Karl Sigmund
since 1978 resulted in the book
**The Theory of Evolution and Dynamical Systems**
(Cambridge University Press 1988)
which presents a unified approach to four different areas
of mathematical biology (population genetics, population ecology,
chemical kinetics of macromolecules, and evolutionary game dynamics)
through its common basic dynamic model:
the Lotka-Volterra and replicator equations.
A largely revised, reorganized and updated edition appeared in May 1998
under the title

** Evolutionary Games and Population Dynamics **
More recently I collaborate with Balázs Boros on chemical reaction networks.

I am/was member of the ** editorial board ** of
Selection ,

the
International Journal of Game Theory ,
Games and Economic Behavior ,

Discrete and Continuous Dynamical Systems - B ,
the Monatshefte für Mathematik, and Games.

For more information see here .

** Member ** of the

Society of the Erwin Schrödinger Institute for Mathematical Physics

and the
The Game Theory Society,

Research fellow at ELSE.

My Erdős number
is 3, see Famous Trails to Paul Erdős (p.14-15).

Finally some links to my recent
publications
(most for downloading),

a list of my graduate students and
collaborators.

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