mathematics

Laurent Bartholdi

Laurent Bartholdi 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 Laurent Bartholdi rather than just read about it. In short: Laurent Bartholdi is a Swiss mathematician working in the areas of geometric group theory, symbolic dynamics, and computational complexity. He is particularly well-known for his contributions to the study of self-similar groups and amenability of groups.

Key takeaways

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

Reference excerpt

Laurent Bartholdi is a Swiss mathematician working in the areas of geometric group theory, symbolic dynamics, and computational complexity. He is particularly well-known for his contributions to the study of self-similar groups and amenability of groups. Currently Bartholdi is a CNRS Directeur de Recherche at Institut Camille Jordan, Claude Bernard University Lyon 1 in France. Bartholdi received a PhD in Mathematics in 2000 from the University of Geneva, with Pierre de la Harpe and Rostislav Grigorchuk as co-advisors. In June 2025 Bartholdi delivered the inaugural Paul Schupp Distinguished Lecture at the GAGTA 2025 "Groups, Logic and Computation" conference at the Stevens Institute of Technology.

Selected works Laurent Bartholdi; Balint Virág (2005). "Amenability via random walks". Duke Mathematical Journal. 130 (1): 39–56. arXiv:math/0305262. doi:10.1215/S0012-7094-05-13012-5. MR 2176547. Laurent Bartholdi (2010). "Gardens of Eden and amenability on cellular automata". Journal of the European Mathematical Society. 12 (1): 241–248. doi:10.4171/JEMS/196. MR 2578610. Laurent Bartholdi; Anna Erschler (2012). "Growth of permutational extensions". Inventiones Mathematicae. 189 (2): 431–455. arXiv:1011.5266. doi:10.1007/s00222-011-0368-x. MR 2947548. Laurent Bartholdi; Dzmitry Dudko (2021). "Algorithmic aspects of branched coverings II/V: sphere bisets and decidability of Thurston equivalence". Inventiones Mathematicae. 223 (3): 895–994. doi:10.1007/s00222-020-00995-2. MR 4213769.

References

External links Laurent Bartholdi's Google Scholar profile Laurent Bartholdi at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Laurent Bartholdi

Start with the simplest possible case. Write down what Laurent Bartholdi 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 Laurent Bartholdi 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 Laurent Bartholdi 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 Laurent Bartholdi

In research: Laurent Bartholdi 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 Laurent Bartholdi 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: Laurent Bartholdi is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century Swiss mathematicians, 21st-century mathematicians, Living people, so understanding it makes those chapters shorter.
In everyday life: Look for Laurent Bartholdi 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 Laurent Bartholdi in 20 minutes

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

Frequently asked questions

What is Laurent Bartholdi in simple terms?

Why does Laurent Bartholdi 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 Laurent Bartholdi?

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 Laurent Bartholdi.