mathematics

Thomas Willwacher

Thomas Willwacher 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 Thomas Willwacher rather than just read about it. In short: Thomas Hans Willwacher (born 12 April 1983) is a German mathematician and mathematical physicist working as a Professor at the Institute of Mathematics, ETH Zurich. Biography Willwacher completed his PhD at ETH Zurich in 2009 with a thesis on "Cyclic Formality", under the supervision of Giovanni Felder, Alberto Cattaneo, and Anton Alekseev.

Key takeaways

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

Reference excerpt

Thomas Hans Willwacher (born 12 April 1983) is a German mathematician and mathematical physicist working as a Professor at the Institute of Mathematics, ETH Zurich.

Biography Willwacher completed his PhD at ETH Zurich in 2009 with a thesis on "Cyclic Formality", under the supervision of Giovanni Felder, Alberto Cattaneo, and Anton Alekseev. He was a Junior member of the Harvard Society of Fellows from 2010 to 2013. He joined the University of Zurich as an assistant professor in 2013, and was promoted to associate professor in 2015.

Research and recognition In July 2016 Willwacher was awarded a prize from the European Mathematical Society for "his striking and important research in a variety of mathematical fields: homotopical algebra, geometry, topology and mathematical physics, including deep results related to Kontsevich's formality theorem and the relation between Kontsevich's graph complex and the Grothendieck-Teichmüller Lie algebra". Notable results of Willwacher include the proof of Maxim Kontsevich's cyclic formality conjecture and the proof that the Grothendieck–Teichmüller Lie algebra is isomorphic to the degree zero cohomology of Kontsevich's graph complex.

References

External links "Homepage at ETH Zurich".

Worked examples

Example 1 — a first encounter with Thomas Willwacher

Start with the simplest possible case. Write down what Thomas Willwacher 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 Thomas Willwacher 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 Thomas Willwacher 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 Thomas Willwacher

In research: Thomas Willwacher 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 Thomas Willwacher 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: Thomas Willwacher is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1983 births, 21st-century German mathematicians, Academic staff of ETH Zurich, so understanding it makes those chapters shorter.
In everyday life: Look for Thomas Willwacher 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 Thomas Willwacher in 20 minutes

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

Frequently asked questions

What is Thomas Willwacher in simple terms?

Thomas Hans Willwacher (born 12 April 1983) is a German mathematician and mathematical physicist working as a Professor at the Institute of Mathematics, ETH Zurich. Biography Willwacher completed his PhD at ETH Zurich in 2009 with a thesis on "Cyclic Formality", under the supervision of Giovanni Fe…

Why does Thomas Willwacher 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 Thomas Willwacher?

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 Thomas Willwacher.