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Jürgen Jost

Jürgen Jost is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Jürgen Jost rather than just read about it. In short: Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.

Jürgen Jost — main illustration
Jürgen Jost — illustration

Key takeaways

  • Jürgen Jost belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Jürgen Jost to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Jürgen Jost from memory before moving on to harder problems.

Reference excerpt

Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.

Life and work In 1975, he began studying mathematics, physics, economics and philosophy. In 1980 he received a Dr. rer. nat. from the University of Bonn under the supervision of Stefan Hildebrandt. In 1984 he was at the University of Bonn for the habilitation. After his habilitation, he was at the Ruhr University Bochum, the chair of Mathematics X, Analysis. During this time he was the coordinator of the project "Stochastic Analysis and systems with infinitely many degrees of freedom" from July 1987 to December 1996. For this work he received the 1993 Gottfried Wilhelm Leibniz Prize, awarded by the Deutsche Forschungsgemeinschaft. Since 1996, he has been director and scientific member at the Max Planck Institute for Mathematics in the Sciences in Leipzig, having left Bochum after more than 10 years of work there, to "tackle new research problems in the border area between mathematics and the natural sciences and simultaneously encourage mathematical research in Germany, particularly in the fields of geometry and analysis." In 1998 he was an honorary professor at the University of Leipzig. In 2002, there, he initiated with two other scientists from the Max Planck Institute, the Interdisciplinary Center for Bioinformatics (IZBI). In 1986 he was invited speaker at the International Congress of Mathematicians in Berkeley (Two dimensional geometric variational problems). He is a fellow of the American Mathematical Society. His research focuses are:

Complex dynamical systems Neural networks Cognitive structures and theoretical neurobiology, cognitive science, theoretical and mathematical biology Riemannian geometry; analysis and geometry Calculus of variations and partial differential equations; mathematical physics

Bibliography Jost, Jürgen (1983). Harmonic mappings between Riemannian manifolds. Canberra: Centre for Mathematical Analysis, Australian National University. ISBN 0-86784-403-5. OCLC 13282393. Jost, Jürgen (1984). "Harmonic Maps Between Surfaces (with a Special Chapter on Conformal Mappings)". Lecture Notes in Mathematics. Vol. 1062. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/bfb0100160. ISBN 978-3-540-13339-1. ISSN 0075-8434. Jost, Jürgen (1988). Nonlinear Methods in Riemannian and Kählerian Geometry : Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986. Basel: Birkhäuser Basel Imprint Birkhäuser. ISBN 978-3-0348-7690-2. OCLC 851812426. Jost, Jürgen (1991). Two-dimensional geometric variational problems. Chichester New York: Wiley. ISBN 978-0-471-92839-3. OCLC 21672946. Differentialgeometrie und Minimalflächen. Berlin, Heidelberg: Springer Berlin Heidelberg. 2007. doi:10.1007/978-3-540-68293-6. ISBN 978-3-540-22227-9. Jost, Jürgen (2017). Riemannian geometry and geometric analysis. Cham, Switzerland: Springer. ISBN 978-3-319-61859-3. OCLC 1007152776. Jost, Jürgen (2006). Compact Riemann Surfaces. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-540-33067-7. ISBN 978-3-540-33065-3. Jost, Jürgen (2005). Postmodern analysis. Berlin: Springer. ISBN 978-3-540-25830-8. OCLC 209870644. Albeverio, Sergio (1997). A mathematical introduction to string theory : variational problems, geometric and probabilistic methods. Cambridge New York: Cambridge University Press. ISBN 978-0-521-55610-1. OCLC 836871453. Jost, Jürgen; Li-Jost, Xianqing (1998). Calculus of variations. Cambridge, UK New York: Cambridge University Press. ISBN 978-0-521-05712-7. OCLC 39658898. Jost, Jürgen (1997). Nonpositive curvature : geometric and analytic aspects. Basel Boston: Birkhäuser. ISBN 978-3-7643-5736-8. OCLC 36761646. Jost, Jürgen (1998). Partielle Differentialgleichungen. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-642-58888-4. ISBN 978-3-540-64222-0. Bosonic Strings: A mathematical treatment, AMS international press, 2001 Jost, Jürgen (2013). "Partial Differential Equations". Graduate Texts in Mathematics. Vol. 214. New York, NY: Springer New York. doi:10.1007/978-1-4614-4809-9. ISBN 978-1-4614-4808-2. ISSN 0072-5285. Jost, Jürgen (2005). Dynamical systems : examples of complex behaviour. Berlin New York: Springer. ISBN 978-3-540-22908-7. OCLC 209861174. Jost, Jürgen (2009). Geometry and physics. Berlin London: Springer. ISBN 978-3-642-00540-4. OCLC 489215723. Ay, Nihat; Jost, Jürgen; Lê, Hông Vân; Schwachhöfer, Lorenz (2017). Information geometry. Cham. ISBN 978-3-319-56477-7. OCLC 1007533823.{{cite book}}: CS1 maint: location missing publisher (link)

References

External links Webpage at Max-Planck-Institut

Illustrations

Jürgen Jost illustration

Worked examples

Example 1 — a first encounter with Jürgen Jost

Start with the simplest possible case. Write down what Jürgen Jost claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Jürgen Jost before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Jürgen Jost ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Jürgen Jost

In research
Jürgen Jost appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Jürgen Jost in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Jürgen Jost is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1956 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Jürgen Jost outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Jürgen Jost in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Jürgen Jost means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Jürgen Jost out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jürgen Jost in simple terms?

Jürgen Jost (born 9 June 1956) is a German mathematician specializing in geometry. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.

Why does Jürgen Jost matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Jürgen Jost?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Jürgen Jost.

Tags

  • 1956 births
  • 20th-century German mathematicians
  • 21st-century German mathematicians
  • Academic staff of Ruhr University Bochum
  • Fellows of the American Mathematical Society
  • German mathematical analysts
  • Living people
  • Max Planck Institute directors
  • Max Planck Institutes researchers
  • University of Bonn alumni
  • Variational analysts

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