mathematics

Victor Bangert

Victor Bangert 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 Victor Bangert rather than just read about it. In short: Victor Bangert (born 28 November 1950) is Professor of Mathematics at the Mathematisches Institut in Freiburg, Germany. His main interests are differential geometry and dynamical systems theory.

Key takeaways

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

Reference excerpt

Victor Bangert (born 28 November 1950) is Professor of Mathematics at the Mathematisches Institut in Freiburg, Germany. His main interests are differential geometry and dynamical systems theory. He specialises in the theory of closed geodesics, wherein one of his significant results, combined with another one due to John Franks, implies that every Riemannian 2-sphere possesses infinitely many closed geodesics. He also made important contributions to Aubry–Mather theory. He obtained his Ph.D. from Universität Dortmund in 1977 under the supervision of Rolf Wilhelm Walter, with the thesis Konvexität in riemannschen Mannigfaltigkeiten. He served in the editorial board of "manuscripta mathematica" from 1996 to 2017. Bangert was an invited speaker at the 1994 International Congress of Mathematicians in Zürich.

Selected publications Bangert, Victor (1980). "Closed geodesics on complete surfaces". Mathematische Annalen. 251 (1). Springer Science and Business Media LLC: 83–96. doi:10.1007/bf01420283. ISSN 0025-5831. S2CID 121131779. Bangert, V.; Klingenberg, W. (1983). "Homology generated by iterated closed geodesics". Topology. 22 (4). Elsevier BV: 379–388. doi:10.1016/0040-9383(83)90033-2. ISSN 0040-9383. Bangert, V. (1988). "Mather Sets for Twist Maps and Geodesics on Tori". Dynamics Reported. Vol. 1. Wiesbaden: Vieweg+Teubner Verlag. pp. 1–56. doi:10.1007/978-3-322-96656-8_1. ISBN 978-3-519-02150-6. ISSN 0936-6040. Bangert, Victor (1990). "Minimal geodesics". Ergodic Theory and Dynamical Systems. 10 (2). Cambridge University Press (CUP): 263–286. doi:10.1017/s014338570000554x. ISSN 0143-3857. S2CID 247631967. Bangert, Victor (1993). "On the Existence of Closed Geodesics on Two-Spheres". International Journal of Mathematics. 04 (1). World Scientific Pub Co Pte Lt: 1–10. doi:10.1142/s0129167x93000029. ISSN 0129-167X. Bangert, Victor (1994). "Geodesic rays, Busemann functions and monotone twist maps". Calculus of Variations and Partial Differential Equations. 2 (1). Springer Science and Business Media LLC: 49–63. doi:10.1007/bf01234315. ISSN 0944-2669. S2CID 120188519. Bangert, Victor; Katz, Mikhail (24 April 2003). "Stable systolic inequalities and cohomology products". Communications on Pure and Applied Mathematics. 56 (7). Wiley: 979–997. arXiv:math/0204181. doi:10.1002/cpa.10082. ISSN 0010-3640. S2CID 14485627. Bangert, Victor; Katz, Mikhail G.; Shnider, Steven; Weinberger, Shmuel (15 January 2009). "E7, Wirtinger inequalities, Cayley 4-form, and homotopy". Duke Mathematical Journal. 146 (1). Duke University Press. arXiv:math/0608006. doi:10.1215/00127094-2008-061. ISSN 0012-7094. S2CID 2575584.

References

Victor Bangert at the Mathematics Genealogy Project Cipra, Barry; Paul Zorn (1993). "Collaboration Closes in on Closed Geodesics". What's happening in the mathematical sciences, Volume 1. American Mathematical Society. p. 27. ISBN 978-0-8218-8999-2. "Prof. Dr. Victor Bangert" (in German). Retrieved 10 September 2010.

External links Personal webpage Oberwolfach photos of Victor Bangert

Illustrations

Worked examples

Example 1 — a first encounter with Victor Bangert

Start with the simplest possible case. Write down what Victor Bangert 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 Victor Bangert 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 Victor Bangert 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 Victor Bangert

In research: Victor Bangert 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 Victor Bangert 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: Victor Bangert is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1950 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Victor Bangert 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Victor Bangert” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Victor Bangert in 20 minutes

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

Frequently asked questions

What is Victor Bangert in simple terms?

Victor Bangert (born 28 November 1950) is Professor of Mathematics at the Mathematisches Institut in Freiburg, Germany. His main interests are differential geometry and dynamical systems theory.

Why does Victor Bangert 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 Victor Bangert?

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 Victor Bangert.