Gerald Teschl

Encyclopedia

**Gerald Teschl**is an Austria

Austria

Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...

n mathematical physicist and Professor

Professor

A professor is a scholarly teacher; the precise meaning of the term varies by country. Literally, professor derives from Latin as a "person who professes" being usually an expert in arts or sciences; a teacher of high rank...

of Mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

.

He is working in the area of mathematical physics

Mathematical physics

Mathematical physics refers to development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines this area as: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and...

; in particular direct and inverse spectral theory

Spectral theory

In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces. It is a result of studies of linear algebra and the solutions of...

with application to completely integrable partial differential equation

Partial differential equation

In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...

s (soliton

Soliton

In mathematics and physics, a soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium...

equations).

## Career

After studying physicsPhysics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

at the Graz University of Technology

Graz University of Technology

The Graz University of Technology is the second largest university in Styria, Austria, after the University of Graz. Austria has three universities of technology – in Graz, in Leoben, and in Vienna. The Graz University of Technology was founded in 1811 by Archduke John of Austria. TUG, as the...

(diploma thesis 1993) he continued with a PhD

PHD

PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...

in Mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

at the University of Missouri – Columbia

University of Missouri

The University of Missouri System is a state university system providing centralized administration for four universities, a health care system, an extension program, five research and technology parks, and a publishing press. More than 64,000 students are currently enrolled at its four campuses...

. The title of his thesis supervised by Fritz Gesztesy

Fritz Gesztesy

Friedrich „Fritz“ Gesztesy is a well-known Austrian-American mathematical physicist and Professor of Mathematics at the University of Missouri, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics , and completely integrable systems...

was

*Spectral Theory for Jacobi Operators*(1995). After a Post doc position at the Rheinisch-Westfälischen Technische Hochschule Aachen

RWTH Aachen

RWTH Aachen University is a research university located in Aachen, North Rhine-Westphalia, Germany with roughly 33,000 students enrolled in 101 study programs....

(1996/97) he moved to Vienna where he received his Habilitation

Habilitation

Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...

at the University of Vienna in May 1998. Since then he is there a professor of mathematics.

In 1997 he received the Ludwig Boltzmann Prize

Ludwig Boltzmann Prize

The Ludwig Boltzmann Prize is awarded by the Austrian Physical Society and honors outstanding achievements in theoretical physics. It is named after the famous austrian physicist Ludwig Boltzmann....

from the Austrian Physical Society

Austrian Physical Society

-History:Until 1938 Austrian physicists were part of the German Physical Society. On December 13, 1950, it was decided to found a separate society for Austria and Fritz Kohlrausch was elected as first president in 1951.-Prizes:...

, 1999 the Prize of the Austrian Mathematical Society

Prize of the Austrian Mathematical Society

The Prize of the Austrian Mathematical Society is the highest mathematics award in Austria. It is awarded every year by the Austrian Mathematical Society to a promising young mathematician for outstanding achievements. A substantial part of the work must have been performed in Austria. The...

. In 2006 he was awarded with the prestigious START-Preis

Start-Preis

The Start-Preis is the highest Austrian award for scientists under the age of 35.It is awarded once per year by the Austrian Science Fund on behalf of the Austrian Ministry for Science....

by the Austrian Science Fund

Austrian Science Fund

The Fonds zur Förderung der wissenschaftlichen Forschung is the most important Austrian funding organization for basic research. The FWF supports research in science, engineering, and the humanities through a large variety of grant programmes, prizes and by funding infrastructure...

(FWF). In 2011 he became a member of the Austrian Academy of Sciences

Austrian Academy of Sciences

The Austrian Academy of Sciences is a legal entity under the special protection of the Federal Republic of Austria. According to the statutes of the Academy its mission is to promote the sciences and humanities in every respect and in every field, particularly in fundamental research...

(ÖAW).

His most important contributions are to the fields of Sturm–Liouville theory, Jacobi operator

Jacobi operator

A Jacobi operator, named after Carl Gustav Jakob Jacobi, is a symmetric linear operator acting on sequences which is given by a tridiagonal matrix in the standard basis given by Kronecker deltas.- Self-adjoint Jacobi operators :...

s and the Toda lattice. He also works in biomathematics, in particular in the novel area of breath gas analysis

Breath gas analysis

Breath gas analysis is a method for gaining non-invasive information on the clinical state of an individual by monitoring volatile organic compounds present in the exhaled breath...

, and has written a successful undergraduate textbook (Mathematics for Computer Science, in German

German language

German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....

) with his wife.

## Selected publications

- with Julian King, Helin Koc, Karl Unterkofler, Pawel Mochalski, Alexander Kupferthaler, Susanne Teschl, Hartmann Hinterhuber, Anton AmannAnton AmannAnton Amann is an Austrian chemist andProfessor of chemistry at the Innsbruck Medical University. He is working in the area of physical chemistry, ECG analysis, and exhaled breath analysis....

:*Physiological modeling of isoprene dynamics in exhaled breath,*J. Theoret. Biol. 267 (2010), 626-637, http://arxiv.org/abs/1010.2145. *Mathematical Methods in Quantum Mechanics with Applications to Schrödinger Operators*, American Mathematical Society, Graduate Studies in Mathematics, Volume 99, 2009, ISBN 9780821846605- with Susanne Teschl:
*Mathematik für Informatiker*, 2 Bände, Springer Verlag, Bd. 1 (Diskrete Mathematik und Lineare Algebra), 3. Auflage 2008, ISBN 9783540774310, Bd. 2 (Analysis und Statistik), 2. Auflage 2007, ISBN 9783540724513 - with Fritz GesztesyFritz GesztesyFriedrich „Fritz“ Gesztesy is a well-known Austrian-American mathematical physicist and Professor of Mathematics at the University of Missouri, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics , and completely integrable systems...

, Helge HoldenHelge HoldenHelge Holden is a Norwegian mathematician working in the field of Differential equations and Mathematical physics.He took the dr.philos. degree at the University of Oslo in 1985. The title of his dissertation with Raphael Høegh-Krohn was Point Interactions and the Short-Range Expansion. A Solvable...

and Johanna Michor:*Soliton Equations and their Algebro-Geometric Solutions*, Volume 2 (*1+1 dimensional discrete models*), Cambridge Studies in Advanced Mathematics Bd.114, Cambridge University Press 2008, ISBN 9780521753081 - with Spyridon Kamvissis:
*Stability of periodic soliton equations under short range perturbations*, Phys. Lett. A 364 (2007), 480–483. *Jacobi Operators and Completely Integrable Nonlinear Lattices*, American Mathematical Society, Mathematical Surveys and Monographs, Volume 72, 2000, ISBN 0821819402- with Fritz GesztesyFritz GesztesyFriedrich „Fritz“ Gesztesy is a well-known Austrian-American mathematical physicist and Professor of Mathematics at the University of Missouri, known for his important contributions in spectral theory, functional analysis, nonrelativistic quantum mechanics , and completely integrable systems...

and Barry SimonBarry SimonBarry Simon is an eminent American mathematical physicist and the IBM Professor of Mathematics and Theoretical Physics at Caltech, known for his prolific contributions in spectral theory, functional analysis, and nonrelativistic quantum mechanics , including the connections to atomic and...

:*Zeros of the Wronskian and renormalized oscillation theory*, Am. J. Math. 118 (1996) 571–594.