mathematics

Miguel Walsh

Miguel Walsh 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 Miguel Walsh rather than just read about it. In short: Miguel Nicolás Walsh is an Argentine mathematician working in number theory and ergodic theory. He is a professor at the University of Buenos Aires.

Key takeaways

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

Reference excerpt

Miguel Nicolás Walsh is an Argentine mathematician working in number theory and ergodic theory. He is a professor at the University of Buenos Aires.

Education and career Walsh has previously held a Clay Research Fellowship and was a fellow of Merton College at the University of Oxford. He is a professor of mathematics at the University of Buenos Aires. He was also Member of the Mathematical Sciences Research Institute at Berkeley, Senior Fellow of the Institute for Pure and Applied Mathematics at UCLA and von Neumann Fellow of the Institute for Advanced Study at Princeton. Walsh was born in Buenos Aires, Argentina. He obtained his undergraduate degree in 2010 from the University of Buenos Aires and his PhD, also from the same institution, in 2012.

Recognition He received the MCA Prize in 2013. In 2014, he was awarded the ICTP Ramanujan Prize for his contributions to mathematics. He is the youngest recipient to date of both awards. In June 2017 Walsh was invited to present his research at the 2018 International Congress of Mathematicians in Rio de Janeiro, Brazil. In 2021, he was selected as Plenary Speaker of the Mathematical Congress of the Americas. In 2024, he was awarded the inaugural IMSA Prize of the Institute of the Mathematical Sciences of America during the Mathematical Waves Conference in Miami. That same year, he received the UMALCA Award of the Mathematical Union of Latin America and the Caribbean. He is one of two 2024 recipients of the Salem Prize, given "for contributions to ergodic theory, analytic number theory, and the development of the polynomial method, including a convergence theorem for nonconventional ergodic averages, bounds on the local Fourier uniformity of multiplicative functions, and bounds on rational points on varieties".

Selected publications Walsh, Miguel N. (2020-11-01). "The polynomial method over varieties". Inventiones Mathematicae. 222 (2): 469–512. arXiv:1811.07865. Bibcode:2020InMat.222..469W. doi:10.1007/s00222-020-00975-6. ISSN 1432-1297. S2CID 119650372. Walsh, Miguel N. (2014-04-29). "The algebraicity of ill-distributed sets". Geometric and Functional Analysis. 24 (3): 959–967. arXiv:1307.0259. doi:10.1007/s00039-014-0286-3. ISSN 1016-443X. S2CID 119695020. Walsh, Miguel N. (2012-01-01). "Norm convergence of nilpotent ergodic averages". Annals of Mathematics. 175 (3): 1667–1688. arXiv:1109.2922. doi:10.4007/annals.2012.175.3.15. S2CID 55768070. Walsh, Miguel N. (2012-07-15). "The inverse sieve problem in high dimensions". Duke Mathematical Journal. 161 (10): 2001–2022. arXiv:1105.1551. doi:10.1215/00127094-1645788. hdl:11336/68296. ISSN 0012-7094. S2CID 119317224.

References

External links Walsh's homepage at the University of Oxford lanacion.com – El matemático argentino Miguel Walsh, de 26 años, ganó el premio Ramanujan (in Spanish) mincyt – Interview with Miguel Walsh ICTP – 2014 Ramanujan Prize Announced

Worked examples

Example 1 — a first encounter with Miguel Walsh

Start with the simplest possible case. Write down what Miguel Walsh 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 Miguel Walsh 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 Miguel Walsh 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 Miguel Walsh

In research: Miguel Walsh 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 Miguel Walsh 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: Miguel Walsh is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1987 births, 21st-century Argentine mathematicians, Academic staff of the University of Buenos Aires, so understanding it makes those chapters shorter.
In everyday life: Look for Miguel Walsh 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 Miguel Walsh in 20 minutes

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

Frequently asked questions

What is Miguel Walsh in simple terms?

Miguel Nicolás Walsh is an Argentine mathematician working in number theory and ergodic theory. He is a professor at the University of Buenos Aires.

Why does Miguel Walsh 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 Miguel Walsh?

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 Miguel Walsh.