mathematics

Peter Teichner

Peter Teichner 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 Peter Teichner rather than just read about it. In short: Peter Teichner (born June 30, 1963 in Bratislava, Czechoslovakia) is a German mathematician and one of the directors of the Max Planck Institute for Mathematics in Bonn. His main areas of work are topology and geometry.

Key takeaways

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

Reference excerpt

Peter Teichner (born June 30, 1963 in Bratislava, Czechoslovakia) is a German mathematician and one of the directors of the Max Planck Institute for Mathematics in Bonn. His main areas of work are topology and geometry.

Life In 1988, Peter Teichner graduated from the University of Mainz with a degree in mathematics. After graduating, he worked for one year in Canada, funded by the "Government of Canada Award", at McMaster University in Hamilton (Ontario). From 1989 to 1990 he was affiliated with the Max Planck Institute for Mathematics. From 1990 to 1992 he worked at the University of Mainz as a research assistant, and in 1992 he received his doctorate with Matthias Kreck as his advisor. The title of his doctoral thesis was Topological four-manifolds with finite fundamental group. With a Feodor Lynen Scholarship from the Humboldt Foundation, he went to UC San Diego from 1992 to 1995 and collaborated with Michael Freedman. In 1995 he worked at the Institut des Hautes Études Scientifiques in Bures-sur-Yvette, France. From 1995 to 1996 he was again at the University of Mainz. From 1996 to 1997 he was at UC Berkeley as a Miller Research Fellow. From 1996 he was an associate professor at UC San Diego, and in 1999 he was granted tenure. He stayed at UC San Diego until 2004, since then he has been a full professor at UC Berkeley, where he retired in 2019. He has been a director at the Max Planck Institute for Mathematics in Bonn since 2008. He has also been the managing director from 2011 until 2019. His students include Arthur Bartels, James Conant, and Christopher Schommer-Pries.

Academic work Peter Teichner's work lies in the field of topology, which deals with qualitative properties of geometric objects. His early achievements were on the classification of 4-manifolds. Together with the Fields medalist Mike Freedman, Peter Teichner made contributions to the classification of 4-manifolds whose fundamental group only grows sub-exponentially. Later in his career, he moved on to study Euclidean and topological field theories. In particular, in an ongoing project, Peter Teichner and Stephan Stolz try to refine the mathematical term quantum field theory in such a way that deformation classes of quantum field theories can be interpreted as a qualitative property of a manifold. More specifically, these should form a cohomology theory. The emerging language should be flexible enough to formulate new physical theories, but also so precise that predictions can be made about the impossibility of certain combinations of space-time and quantum fields. This is known as the Stolz-Teichner program.

References

External links Official website

Illustrations

Worked examples

Example 1 — a first encounter with Peter Teichner

Start with the simplest possible case. Write down what Peter Teichner 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 Peter Teichner 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 Peter Teichner 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 Peter Teichner

In research: Peter Teichner 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 Peter Teichner 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: Peter Teichner is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1963 births, 21st-century German mathematicians, German topologists, so understanding it makes those chapters shorter.
In everyday life: Look for Peter Teichner 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 Peter Teichner in 20 minutes

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

Frequently asked questions

What is Peter Teichner in simple terms?

Why does Peter Teichner 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 Peter Teichner?

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 Peter Teichner.