mathematics

Ursula Hamenstädt

Ursula Hamenstädt 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 Ursula Hamenstädt rather than just read about it. In short: Ursula Hamenstädt (born 15 January 1961) is a German mathematician who works as a professor at the University of Bonn. Her primary research subject is differential geometry.

Key takeaways

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

Reference excerpt

Ursula Hamenstädt (born 15 January 1961) is a German mathematician who works as a professor at the University of Bonn. Her primary research subject is differential geometry.

Education and career Hamenstädt earned her PhD from the University of Bonn in 1986, under the supervision of Wilhelm Klingenberg. Her dissertation, Zur Theorie der Carnot-Caratheodory Metriken und ihren Anwendungen [The theory of Carnot–Caratheodory metrics and their applications], concerned the theory of sub-Riemannian manifolds. After completing her doctorate, she became a Miller Research Fellow at the University of California, Berkeley and then an assistant professor at the California Institute of Technology before returning to Bonn as a faculty member in 1990.

Honors Hamenstädt was an invited speaker at the International Congress of Mathematicians in 2010. In 2012 she was elected to the German Academy of Sciences Leopoldina, and in the same year she became one of the inaugural fellows of the American Mathematical Society. She was the Emmy Noether Lecturer of the German Mathematical Society in 2017.

Selected publications Hamenstädt, Ursula (2008). "Geometry of the mapping class groups I: Boundary amenability". Inventiones Mathematicae. 175 (3): 545–609. arXiv:math/0510116. Bibcode:2009InMat.175..545H. doi:10.1007/s00222-008-0158-2. ISSN 0020-9910. S2CID 2640202. Hamenstädt, Ursula (1989). "A new description of the Bowen–Margulis measure". Ergodic Theory and Dynamical Systems. 9 (3): 455–464. doi:10.1017/S0143385700005095. ISSN 1469-4417. Hamenstädt, Ursula (1990). "Some regularity theorems for Carnot–Carathéodory metrics". Journal of Differential Geometry. 32 (3): 819–850. doi:10.4310/jdg/1214445536. ISSN 0022-040X.

References

External links Home page

Illustrations

Worked examples

Example 1 — a first encounter with Ursula Hamenstädt

Start with the simplest possible case. Write down what Ursula Hamenstädt 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 Ursula Hamenstädt 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 Ursula Hamenstädt 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 Ursula Hamenstädt

In research: Ursula Hamenstädt 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 Ursula Hamenstädt 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: Ursula Hamenstädt is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1961 births, 20th-century German mathematicians, 20th-century German women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ursula Hamenstädt 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 Ursula Hamenstädt in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ursula Hamenstädt 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 Ursula Hamenstädt out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ursula Hamenstädt in simple terms?

Ursula Hamenstädt (born 15 January 1961) is a German mathematician who works as a professor at the University of Bonn. Her primary research subject is differential geometry.

Why does Ursula Hamenstädt 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 Ursula Hamenstädt?

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 Ursula Hamenstädt.